Projectile Motion, A study of height and time

[mmiller39]

A Cutnell and Johnson Physics question illustrates a rocket launch:

A rocket is fired at a speed of 97.0 m/s from ground level, at an angle of 53.0 ° above the horizontal. The rocket is fired toward an 27.0-m high wall, which is located 24.0 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?

My Calculations:

Vo = 97.0 m/s
Theta = 53 degrees
x = 24 m
y = 27 m
Let H illustrate the height of the rocket at point x on the axis.
t = ?
a = -9.80 m/s ^2

Vo sin 53 = Voy = 77.46
Vo cos 53 = Vox = 58.37

x = Vox(t)
t = x/Vox = 24/58.37 = .411 s

H = Voy(t) + .5 a(t^2)

Plug and Chug

H = 77.46(.411) + .5(-9.80)(.411^2) = 31 m

Distance Rocket clears wall = 31m-27m = 4.00 m <-----Incorrect.

Is there a problem with my calculations that I am not understanding?

 

[blackwizard]

How do u no ur wrong? Looks ok 2 me unless I am makin exactly the same mistake. Mayb ur lookin under the wrong chapter at the back of the book 4 ur answers!?

 

[kyle8921]

It looks like your calculations are correct, but it's possible that there is an error in the given information. The rocket's initial velocity and angle seem reasonable for a rocket launch, but the height and distance of the wall may not be accurate. It's also possible that the rocket's engines do not shut down immediately after launch, which could affect the calculations. It's always important to double check the given information and assumptions when solving physics problems.