1). A rock climber throws a small first aid kit to another climber who is higher
ID: 1588443 • Letter: 1
Question
1). A rock climber throws a small first aid kit to another climber who is higher up the mountain. The initial velocity of the kit is 11.5 m/s at an angle of 64.0° above the horizontal. At the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero. What is the vertical height difference between the two climbers?
2). A rocket is fired at a speed of 79.9 m/s from ground level, at an angle of 60.4° above the horizontal. The rocket is fired toward an 10.1 m high wall, which is located 26.1 m away. By how much does the rocket clear the top of the wall?
3). A force vector points at an angle of 54.6° above the +x axis. It has a y component of +288 newtons. Calculate the magnitude of the force vector.
Explanation / Answer
1)
along vertical
initial velocity = voy = vo8sintheta = 11.5*sin64
acceleration ay = -g = -9.8 m/s^2
final vertical velocity vy = 0
from equation of motion
vy^2 - voy^2 = 2*ay*y
0 - (11.5*sin64)^2 = -2*9.81*y
y = 5.44 m <<-------answer
(2)
along horizantal
x = vox*t
t = x/vox = x/(vo*costheta)
along vertical
y = voy*t + 0.5*ay*t^2
y = (vo*sintheta*x/(vo*costheta)) - (0.5*g*x^2/(vo^2*(costheta)^2)
y = x*tantheta - 0.5*g*x^2/(vo^2*(costheta)^2)
y = (26.1*tan60.4)-(0.5*9.81*26.1^2)/(79.9^2*(cos60.4)^2)
y = 43.8 m
the rocket clears by 43.8-10.1 = 33.7 m
----
3)
y = a*sintheta
288 = a*sin54.6
a = 353.32 N <<--------answer
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