A test rocket has mass of 50.0kg and is initially at rest on an inclined surface

Question

A test rocket has mass of 50.0kg and is initially at rest on an inclined surface that rises 35.0 degrees above horizontal. It is launched by applying a force of 2380 N parallel to the inclined surface, which accelerates it along a 200-m incline (starting from rest and at point A.) There is no friction between the rocket and the incline. The instant the rocket leaves the incline, its engines are turned off, it is subject only to gravity, and air resistance can be ignored.

A. What is the rocket acceleration? _____ m/s^2

B. What is the rocket’s velocity (magnitude) when it leaves the incline? _____ m/s

C. Find the maximum height above the ground that the rocket reaches. _____m

D. Find the greatest horizontal range of the rocket beyond point A. ______ m

Explanation / Answer

acceleration a = F/m

A)

a = F/m = 2380/50 = 47.6 m/s^2

B)

speed of the rocket after v = sqrt(2*a*s) = sqrt(2*47.6*200) = 138 m/s

C)

alongvertical

speed at A = v0y = v*sin35 = 79.15 m/s

height of A , yo = 200*sin35

at the maximumheight vy = 0

from equation

vy^2 - v0y^2 = 2*ay*dy

0 - 79.15^2 = -2*9.8*(y-(200*sin35))

y = 434.34 m <<<<-------answer

++++++

D)

along vertical

after landing on ground

-yo = voy*T - 0.5*ay*T^2

-(200*sin35) = 79.15*T - (0.5*9.8*T^2)

T = 17.5 s

along horizantal

ax = 0

x = vox*T

x = 138*cos35*17.5

x = 1978.25 m <<--answer

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