Posted by tiffany on Sunday, February 7, 2010 at 8:45pm.
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 61.2° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 20.5 m away. The rocket attains its launch speed in a negligibly short period of time, after which its engines shut down and the rocket coasts. By how much does the rocket clear the top of the wall?

Physics I  MathMate, Sunday, February 7, 2010 at 10:00pm
We will neglect air resistance and propulsion of the rocket, and treat the rocket as a projectile.
v0=initial velocity = 75 m s1
θ=angle with horizontal
horizontal component of velocity, vh
=v0cos θ
Distance from the wall, D = 20.5 m
Time to reach the wall, t1
= D/vh
Vertical component of initial velocity
= vv
= v sin θ
Height h of rocket after time t1
= vv*t1 g (t1)²
Clearance from the wall, C
= h  11m
I get about 23m.

Physics I  brittany, Sunday, February 7, 2010 at 10:17pm
23m is wrong

Physics Icorrection  MathMate, Sunday, February 7, 2010 at 11:23pm
Thank you Brittany, there was a factor (1/2) missing near the end. Here is the corrected calculation.
Height h of rocket after time t1
= vv*t1 (1/2)g(t1)²
Clearance from the wall, C
= h  11m
I get a little less than 25m using g=9.8 m s2.
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