fisica1-youn-e-freedman-exercicios-resolvidos

3.67: Take + y to be downward.
a) Use the vertical motion of the boulder to find the time it takes it to fall 20 m to the
level of the surface of the water.
2
v = , a = 9.80 m/s , y − y = 20 m, t ?
0 y
0
y
0
=
1 2
y − y0 = v0
y
t +
2
a
yt
gives t = 2.02 s
The rock must travel 100 m horizontally during this time, so
x − x0
100 m
v0 x
= = = 49 m/s.
t 2.20 s
b) The rock travels downward 45 m in going from the cliff to the plain. Use this
vertical motion to find the time:
2
v = , a = 9.80 m/s , y − y = 45 m, t ?
0 y
0
y
0
=
1 2
y − y0 = v0
y
t +
2
a
yt
gives t = 3.03s
During this time the rock travels horizontally
x − x0 = v0
x
t = (49 m/s)(3.03s) = 150 m
The rock lands 50 m past the foot of the dam.
3.68: (a) When she catches the bagels, Henrietta has been jogging for 9.00 s plus the time
for the bagels to fall 43.9 m from rest. Get the time to fall:
1 y = gt
2
2
1
43.9 m = (9.80 m/s 2 ) t
2
2
t = 2.99 s
So she has been jogging for 9 .00 s + 2.99 s = 12.0 s . During this time she has gone
x = vt = ( 3.05 m/s)(12.0s) = 36.6 m . Bruce must throw the bagels so they travel 36.6 m
horizontally in 2.99 s
x = vt
36 .6 m = v(2.
99 s)
v = 12.2 m/s
(b) 36.6 m from the building.