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 s-1

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 I-correction -
**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 s-2.

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