Problemas_Cap3

•
UFPR

Agendaufpr
31/03/2022
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Execicio Fisica 1

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Prévia do material em texto
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
1 / 12
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
xB = L− v0x t, yB = H − v0y t−
1
2
g t2
1 / 12
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
xB = L− v0x t, yB = H − v0y t−
1
2
g t2
v0y
v0x
=
H
L
1 / 12
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
xB = L− v0x t, yB = H − v0y t−
1
2
g t2
v0y
v0x
=
H
L
xA = xB ⇒ t =
1 / 12
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
xB = L− v0x t, yB = H − v0y t−
1
2
g t2
v0y
v0x
=
H
L
xA = xB ⇒ t =
L
2v0x
1 / 12
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
xB = L− v0x t, yB = H − v0y t−
1
2
g t2
v0y
v0x
=
H
L
xA = xB ⇒ t =
L
2v0x
yA = v0y
L
2v0x
−
1
2
g
(
L
2v0x
)
2
=
1 / 12
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
xB = L− v0x t, yB = H − v0y t−
1
2
g t2
v0y
v0x
=
H
L
xA = xB ⇒ t =
L
2v0x
yA = v0y
L
2v0x
−
1
2
g
(
L
2v0x
)
2
=
1
2
H −
1
2
g
(
L
2v0x
)
2
yB = H − v0y
L
2v0x
−
1
2
g
(
L
2v0x
)
2
=
1 / 12
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
xB = L− v0x t, yB = H − v0y t−
1
2
g t2
v0y
v0x
=
H
L
xA = xB ⇒ t =
L
2v0x
yA = v0y
L
2v0x
−
1
2
g
(
L
2v0x
)
2
=
1
2
H −
1
2
g
(
L
2v0x
)
2
yB = H − v0y
L
2v0x
−
1
2
g
(
L
2v0x
)
2
= H −
1
2
H −
1
2
g
(
L
2v0x
)
2
=
1 / 12
Problema 28
xA = v0x t, yA = v0y t−
1
2
g t2
xB = L− v0x t, yB = H − v0y t−
1
2
g t2
v0y
v0x
=
H
L
xA = xB ⇒ t =
L
2v0x
yA = v0y
L
2v0x
−
1
2
g
(
L
2v0x
)
2
=
1
2
H −
1
2
g
(
L
2v0x
)
2
yB = H − v0y
L
2v0x
−
1
2
g
(
L
2v0x
)
2
= H −
1
2
H −
1
2
g
(
L
2v0x
)
2
= yA
1 / 12
Problema 51
~r = At î+ (Bt− Ct2)ĵ
2 / 12
Problema 51
~r = At î+ (Bt− Ct2)ĵ
A = 30 m/s, B = 40 m/s, C = 5, 0 m/s2
2 / 12
Problema 51
~r = At î+ (Bt− Ct2)ĵ
A = 30 m/s, B = 40 m/s, C = 5, 0 m/s2
~v =
d~r
dt
= A î+ (B − 2Ct)ĵ
2 / 12
Problema 51
~r = At î+ (Bt− Ct2)ĵ
A = 30 m/s, B = 40 m/s, C = 5, 0 m/s2
~v =
d~r
dt
= A î+ (B − 2Ct)ĵ
~a =
d~v
dt
= −2Cĵ
2 / 12
Problema 51
~r = At î+ (Bt− Ct2)ĵ
A = 30 m/s, B = 40 m/s, C = 5, 0 m/s2
~v =
d~r
dt
= A î+ (B − 2Ct)ĵ
~a =
d~v
dt
= −2Cĵ
t = 10 s
2 / 12
Problema 51
~r = At î+ (Bt− Ct2)ĵ
A = 30 m/s, B = 40 m/s, C = 5, 0 m/s2
~v =
d~r
dt
= A î+ (B − 2Ct)ĵ
~a =
d~v
dt
= −2Cĵ
t = 10 s
~r = (3, 0̂i − 1, 0ĵ) · 102 m,
2 / 12
Problema 51
~r = At î+ (Bt− Ct2)ĵ
A = 30 m/s, B = 40 m/s, C = 5, 0 m/s2
~v =
d~r
dt
= A î+ (B − 2Ct)ĵ
~a =
d~v
dt
= −2Cĵ
t = 10 s
~r = (3, 0̂i − 1, 0ĵ) · 102 m, ~v = (30̂i − 60ĵ) m/s,
2 / 12
Problema 51
~r = At î+ (Bt− Ct2)ĵ
A = 30 m/s, B = 40 m/s, C = 5, 0 m/s2
~v =
d~r
dt
= A î+ (B − 2Ct)ĵ
~a =
d~v
dt
= −2Cĵ
t = 10 s
~r = (3, 0̂i − 1, 0ĵ) · 102 m, ~v = (30̂i − 60ĵ) m/s, ~a = −10ĵ m/s2
2 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
3 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2,
3 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m,
3 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
3 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
t = 6, 0 s
3 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
t = 6, 0 s
~rA = 1, 2 · 10
2 î m,
3 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
t = 6, 0 s
~rA = 1, 2 · 10
2 î m, ~rB = (40 − 36)ĵ m = 4ĵ m
3 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
t = 6, 0 s
~rA = 1, 2 · 10
2 î m, ~rB = (40 − 36)ĵ m = 4ĵ m
~rBA = ~rB − ~rA = (−1, 2 · 10
2 î+ 4ĵ) m
3 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
t = 6, 0 s
4 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
t = 6, 0 s
~vB =
d~rB
dt
= ~aBt = −12ĵ m/s
4 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
t = 6, 0 s
~vB =
d~rB
dt
= ~aBt = −12ĵ m/s
~vBA = ~vB − ~vA = −(20̂i+ 12ĵ) m/s
4 / 12
Problema 61
~rA = ~vAt, ~vA = 20̂i m/s
~rB = ~r0B +
1
2
~aBt
2, ~r0B = 40ĵ m, ~aB = −2, 0ĵ m/s
2
t = 6, 0 s
~vB =
d~rB
dt
= ~aBt = −12ĵ m/s
~vBA = ~vB − ~vA = −(20̂i+ 12ĵ) m/s
~aBA = ~aB − ~aA = −2, 0ĵ m/s
2
4 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2,
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
2 · 4, 90 m/s
9, 81 m/s2
=
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
2 · 4, 90 m/s
9, 81 m/s2
= 0, 999 s
(b)
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
2 · 4, 90 m/s
9, 81 m/s2
= 0, 999 s
(b)
ts =
v0y
g
,
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
2 · 4, 90 m/s
9, 81 m/s2
= 0, 999 s
(b)
ts =
v0y
g
, ∆y =
v2
0y
2g
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
2 · 4, 90 m/s
9, 81 m/s2
= 0, 999 s
(b)
ts =
v0y
g
, ∆y =
v2
0y
2g
∆~r = ∆yĵ =
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
2 · 4, 90 m/s
9, 81 m/s2
= 0, 999 s
(b)
ts =
v0y
g
, ∆y =
v2
0y
2g
∆~r = ∆yĵ =
v2
0y
2g
ĵ =
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
2 · 4, 90 m/s
9, 81 m/s2
= 0, 999 s
(b)
ts =
v0y
g
, ∆y =
v2
0y
2g
∆~r = ∆yĵ =
v2
0y
2g
ĵ =
4, 902 (m/s)2
2 · 9, 81 m/s2
ĵ =
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(a)
∆y = v0yt−
1
2
gt2, t =
2v0y
g
=
2 · 4, 90 m/s
9, 81 m/s2
= 0, 999 s
(b)
ts =
v0y
g
, ∆y =
v2
0y
2g
∆~r = ∆yĵ =
v2
0y
2g
ĵ =
4, 902 (m/s)2
2 · 9, 81 m/s2
ĵ = 1, 22ĵ m
5 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c)
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 =
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 = 20, 6 m/s
(d)
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 = 20, 6 m/s
(d)
θ0 = arctan
v0y
vx
= arctan
4, 90
20, 0
=
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 = 20, 6 m/s
(d)
θ0 = arctan
v0y
vx
= arctan
4, 90
20, 0
= 13, 8◦
(e)
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 = 20, 6 m/s
(d)
θ0 = arctan
v0y
vx
= arctan
4, 90
20, 0
= 13, 8◦
(e)
∆~r = ∆xî+∆yĵ
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 = 20, 6 m/s
(d)
θ0 = arctan
v0y
vx
= arctan
4, 90
20, 0
= 13, 8◦
(e)
∆~r = ∆xî+∆yĵ
∆x = vxts = vx
v0y
g
=
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 = 20, 6 m/s
(d)
θ0 = arctan
v0y
vx
= arctan
4, 90
20, 0
= 13, 8◦
(e)
∆~r = ∆xî+∆yĵ
∆x = vxts = vx
v0y
g
= 20, 0 m/s
4, 90 m/s
9, 81 m/s2
=
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 = 20, 6 m/s
(d)
θ0 = arctan
v0y
vx
= arctan
4, 90
20, 0
= 13, 8◦
(e)
∆~r = ∆xî+∆yĵ
∆x = vxts = vx
v0y
g
= 20, 0 m/s
4, 90 m/s
9, 81 m/s2
= 9, 99 m
6 / 12
Problema 64
vx = 20, 0 m/s, v0y = 4, 90 m/s
(c) v0 =
√
v2x + v
2
0y =
√
20, 02 + 4, 902 = 20, 6 m/s
(d)
θ0 = arctanv0y
vx
= arctan
4, 90
20, 0
= 13, 8◦
(e)
∆~r = ∆xî+∆yĵ
∆x = vxts = vx
v0y
g
= 20, 0 m/s
4, 90 m/s
9, 81 m/s2
= 9, 99 m
∆~r = (9, 99̂i + 1, 22ĵ) m
6 / 12
Problema 67(a)
T = 24 h, R = 6, 370 · 103 km
7 / 12
Problema 67(a)
T = 24 h, R = 6, 370 · 103 km
v =
2πR
T
=
7 / 12
Problema 67(a)
T = 24 h, R = 6, 370 · 103 km
v =
2πR
T
=
2 · π · 6, 37 · 103 km
24 h
=
7 / 12
Problema 67(a)
T = 24 h, R = 6, 370 · 103 km
v =
2πR
T
=
2 · π · 6, 37 · 103 km
24 h
= 1, 7 · 103 km/h
7 / 12
Problema 67(a)
T = 24 h, R = 6, 370 · 103 km
v =
2πR
T
=
2 · π · 6, 37 · 103 km
24 h
= 1, 7 · 103 km/h
ac =
v2
R
=
7 / 12
Problema 67(a)
T = 24 h, R = 6, 370 · 103 km
v =
2πR
T
=
2 · π · 6, 37 · 103 km
24 h
= 1, 7 · 103 km/h
ac =
v2
R
=
1, 72 · 106 (km/h)2
6, 37 · 103 km
=
7 / 12
Problema 67(a)
T = 24 h, R = 6, 370 · 103 km
v =
2πR
T
=
2 · π · 6, 37 · 103 km
24 h
= 1, 7 · 103 km/h
ac =
v2
R
=
1, 72 · 106 (km/h)2
6, 37 · 103 km
= 4, 5 · 102 km/h2
= 4, 5 · 102
103 m
36002 s2
=
7 / 12
Problema 67(a)
T = 24 h, R = 6, 370 · 103 km
v =
2πR
T
=
2 · π · 6, 37 · 103 km
24 h
= 1, 7 · 103 km/h
ac =
v2
R
=
1, 72 · 106 (km/h)2
6, 37 · 103 km
= 4, 5 · 102 km/h2
= 4, 5 · 102
103 m
36002 s2
= 0, 035 m/s2
7 / 12
Problema 67(c)
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ =
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ = 5, 2 · 103 km
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ = 5, 2 · 103 km
v =
2πR
T
=
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ = 5, 2 · 103 km
v =
2πR
T
=
2 · π · 5, 2 · 103 km
24 h
=
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ = 5, 2 · 103 km
v =
2πR
T
=
2 · π · 5, 2 · 103 km
24 h
= 1, 4 · 103 km/h
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ = 5, 2 · 103 km
v =
2πR
T
=
2 · π · 5, 2 · 103 km
24 h
= 1, 4 · 103 km/h
ac =
v2
R
=
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ = 5, 2 · 103 km
v =
2πR
T
=
2 · π · 5, 2 · 103 km
24 h
= 1, 4 · 103 km/h
ac =
v2
R
=
1, 42 · 106 (km/h)2
5, 2 · 103 km
=
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ = 5, 2 · 103 km
v =
2πR
T
=
2 · π · 5, 2 · 103 km
24 h
= 1, 4 · 103 km/h
ac =
v2
R
=
1, 42 · 106 (km/h)2
5, 2 · 103 km
= 3, 8 · 102 km/h2
= 3, 8 · 102
103 m
36002 s2
=
8 / 12
Problema 67(c)
R = 6, 37 · 103 km cos 35◦ = 5, 2 · 103 km
v =
2πR
T
=
2 · π · 5, 2 · 103 km
24 h
= 1, 4 · 103 km/h
ac =
v2
R
=
1, 42 · 106 (km/h)2
5, 2 · 103 km
= 3, 8 · 102 km/h2
= 3, 8 · 102
103 m
36002 s2
= 0, 029 m/s2
8 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
9 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
y = H + v0yt−
1
2
gt2 =
9 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
y = H + v0yt−
1
2
gt2 = H + (v0 sin θ)t−
1
2
gt2 = 0
9 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
y = H + v0yt−
1
2
gt2 = H + (v0 sin θ)t−
1
2
gt2 = 0
t =
1
g
(
v0 sin θ +
√
v2
0
sin2 θ + 2gH
)
9 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
y = H + v0yt−
1
2
gt2 = H + (v0 sin θ)t−
1
2
gt2 = 0
t =
1
g
(
v0 sin θ +
√
v2
0
sin2 θ + 2gH
)
vx = v0 cos θ,
9 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
y = H + v0yt−
1
2
gt2 = H + (v0 sin θ)t−
1
2
gt2 = 0
t =
1
g
(
v0 sin θ +
√
v2
0
sin2 θ + 2gH
)
vx = v0 cos θ, vy = v0 sin θ − gt =
9 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
y = H + v0yt−
1
2
gt2 = H + (v0 sin θ)t−
1
2
gt2 = 0
t =
1
g
(
v0 sin θ +
√
v2
0
sin2 θ + 2gH
)
vx = v0 cos θ, vy = v0 sin θ − gt = −
√
v2
0
sin2 θ + 2gH
9 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
y = H + v0yt−
1
2
gt2 = H + (v0 sin θ)t−
1
2
gt2 = 0
t =
1
g
(
v0 sin θ +
√
v2
0
sin2 θ + 2gH
)
vx = v0 cos θ, vy = v0 sin θ − gt = −
√
v2
0
sin2 θ + 2gH
v2 = v2x + v
2
y = (1, 2 · v0)
2
9 / 12
Problema 74
θ = 30◦, H = 40 m, vf = 1, 2v0
y = H + v0yt−
1
2
gt2 = H + (v0 sin θ)t−
1
2
gt2 = 0
t =
1
g
(
v0 sin θ +
√
v2
0
sin2 θ + 2gH
)
vx = v0 cos θ, vy = v0 sin θ − gt = −
√
v2
0
sin2 θ + 2gH
v2 = v2x + v
2
y = (1, 2 · v0)
2
v2
0
cos2 θ + v2
0
sin2 θ + 2gH = 1, 44v2
0
9 / 12
Problema 74
v20 + 2gH = 1, 44v
2
0
Resposta não depende de θ
10 / 12
Problema 74
v20 + 2gH = 1, 44v
2
0
Resposta não depende de θ
0, 44v2
0
= 2gH,
10 / 12
Problema 74
v20 + 2gH = 1, 44v
2
0
Resposta não depende de θ
0, 44v2
0
= 2gH, v0 =
√
2gH
0, 44
=
10 / 12
Problema 74
v20 + 2gH = 1, 44v
2
0
Resposta não depende de θ
0, 44v2
0
= 2gH, v0 =
√
2gH
0, 44
=
√
2 · 9, 81 m/s2 · 40 m
0, 44
=
10 / 12
Problema 74
v20 + 2gH = 1, 44v
2
0
Resposta não depende de θ
0, 44v2
0
= 2gH, v0 =
√
2gH
0, 44
=
√
2 · 9, 81 m/s2 · 40 m
0, 44
= 42 m/s
10 / 12
Problema 83
H = 24 m, R = 18 m
(a)
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
=
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
=
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
=
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
= 8, 1 m/s
(b)
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
= 8, 1 m/s
(b)
vy = −gt =
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
= 8, 1 m/s
(b)
vy = −gt = − g
√
2H
g
=
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
= 8, 1 m/s
(b)
vy = −gt = − g
√
2H
g
= −
√
2Hg
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
= 8, 1 m/s
(b)
vy = −gt = − g
√
2H
g
= −
√
2Hg
v =
√
v2
0
+ v2y =
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
= 8, 1 m/s
(b)
vy = −gt = − g
√
2H
g
= −
√
2Hg
v =
√
v2
0
+ v2y =
√
v2
0
+ 2Hg =
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
= 8, 1 m/s
(b)
vy = −gt = − g
√
2H
g
= −
√
2Hg
v =
√
v2
0
+ v2y =
√
v2
0
+ 2Hg =
√
8, 12 + 2 · 24 · 9.81 =
11 / 12
Problema 83
H = 24 m, R = 18 m
(a)
y = H −
1
2
gt2, t =
√
2H
g
R = v0t, v0 =
R
t
= R
√
g
2H
= 18 m
√
9, 81 m/s2
2 · 24 m
= 8, 1 m/s
(b)
vy = −gt = − g
√
2H
g
= −
√
2Hg
v =
√
v2
0
+ v2y =
√
v2
0
+ 2Hg =
√
8, 12 + 2 · 24 · 9.81 = 23 m/s
11 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t,
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
50, 00 m
25, 0 m/s cos 30, 0◦
=
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
50, 00 m
25, 0 m/s cos 30, 0◦
= 2, 31 s
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
50, 00 m
25, 0 m/s cos 30, 0◦
= 2, 31 s
y = (v0 sin θ0)t−
1
2
gt2 =
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
50, 00 m
25, 0 m/s cos 30, 0◦
= 2, 31 s
y = (v0 sin θ0)t−
1
2
gt2 = (25, 0 sin 30, 0◦)2, 31−
1
2
9, 81·2, 312 =
12 / 12Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
50, 00 m
25, 0 m/s cos 30, 0◦
= 2, 31 s
y = (v0 sin θ0)t−
1
2
gt2 = (25, 0 sin 30, 0◦)2, 31−
1
2
9, 81·2, 312 = 2, 7 m
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
50, 00 m
25, 0 m/s cos 30, 0◦
= 2, 31 s
y = (v0 sin θ0)t−
1
2
gt2 = (25, 0 sin 30, 0◦)2, 31−
1
2
9, 81·2, 312 = 2, 7 m
R =
v2
0
g
sin(2θ0) =
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
50, 00 m
25, 0 m/s cos 30, 0◦
= 2, 31 s
y = (v0 sin θ0)t−
1
2
gt2 = (25, 0 sin 30, 0◦)2, 31−
1
2
9, 81·2, 312 = 2, 7 m
R =
v2
0
g
sin(2θ0) =
25, 02 (m/s)2
9, 81 m/s2
sin(60, 0◦) =
12 / 12
Problema 87
L = 50, 0 m, Hg = 3, 05 m, v0 = 25, 0 m/s, θ0 = 30, 0
◦
(a)
L = (v0 cos θ0)t, t =
L
v0 cos θ0
=
50, 00 m
25, 0 m/s cos 30, 0◦
= 2, 31 s
y = (v0 sin θ0)t−
1
2
gt2 = (25, 0 sin 30, 0◦)2, 31−
1
2
9, 81·2, 312 = 2, 7 m
R =
v2
0
g
sin(2θ0) =
25, 02 (m/s)2
9, 81 m/s2
sin(60, 0◦) = 55, 2 m
12 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t,
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t, t =
L
v0 cos θ0
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t, t =
L
v0 cos θ0
y = (v0 sin θ0)t−
1
2
gt2 =
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t, t =
L
v0 cos θ0
y = (v0 sin θ0)t−
1
2
gt2 =
(v0 sin θ0)L
v0 cos θ0
−
1
2
g
(
L
v0 cos θ0
)
2
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t, t =
L
v0 cos θ0
y = (v0 sin θ0)t−
1
2
gt2 =
(v0 sin θ0)L
v0 cos θ0
−
1
2
g
(
L
v0 cos θ0
)
2
= L tan θ0 −
1
2
g
(
L
v0 cos θ0
)
2
= h
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t, t =
L
v0 cos θ0
y = (v0 sin θ0)t−
1
2
gt2 =
(v0 sin θ0)L
v0 cos θ0
−
1
2
g
(
L
v0 cos θ0
)
2
= L tan θ0 −
1
2
g
(
L
v0 cos θ0
)
2
= h
v0 =
L
cos θ0
√
g
2(L tan θ0 − h)
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t, t =
L
v0 cos θ0
y = (v0 sin θ0)t−
1
2
gt2 =
(v0 sin θ0)L
v0 cos θ0
−
1
2
g
(
L
v0 cos θ0
)
2
= L tan θ0 −
1
2
g
(
L
v0 cos θ0
)
2
= h
v0 =
L
cos θ0
√
g
2(L tan θ0 − h)
v0 =
8, 0
cos 30◦
√
9, 81
2(8, 0 tan 30◦ − 4, 0)
=
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t, t =
L
v0 cos θ0
y = (v0 sin θ0)t−
1
2
gt2 =
(v0 sin θ0)L
v0 cos θ0
−
1
2
g
(
L
v0 cos θ0
)
2
= L tan θ0 −
1
2
g
(
L
v0 cos θ0
)
2
= h
v0 =
L
cos θ0
√
g
2(L tan θ0 − h)
v0 =
8, 0
cos 30◦
√
9, 81
2(8, 0 tan 30◦ − 4, 0)
= 26 m/s =
13 / 12
Problema 115
L = 8, 0 m, θ = 30◦, h = 4, 0 m
L = (v0 cos θ0)t, t =
L
v0 cos θ0
y = (v0 sin θ0)t−
1
2
gt2 =
(v0 sin θ0)L
v0 cos θ0
−
1
2
g
(
L
v0 cos θ0
)
2
= L tan θ0 −
1
2
g
(
L
v0 cos θ0
)
2
= h
v0 =
L
cos θ0
√
g
2(L tan θ0 − h)
v0 =
8, 0
cos 30◦
√
9, 81
2(8, 0 tan 30◦ − 4, 0)
= 26 m/s = 94 km/h
13 / 12
Problemas_Cap3

UFPR

Execicio Fisica 1

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