Finding Speed of rocket when altitude is 5.8 m

[staceyrho]

This may be a simple problem, but I'm getting thrown off by the altitude part. Can anyone assist.

A rocket is launched at an angle of 45.8degrees to the horizontal from an altitude of 11.6 m with a speed of 6.48 m/s.

The acceleration of gravity is 9.8 m/s^2. Use energy methods to find it's speed when it's altitude is 5.8 m. Answer in units of m/s.

 

[skeeter]

change in kinetic energy = the opposite of the change in gravitational potential energy

\(\displaystyle \L \frac{1}{2}mv_f^2 - \frac{1}{2}mv_o^2 = -(mgh_f - mgh_o)\)

masses all cancel ...

\(\displaystyle \L \frac{1}{2}(v_f^2 - v_o^2) = g(h_o - h_f)\)

\(\displaystyle \L v_f^2 - v_o^2 = 2g(h_o - h_f)\)

\(\displaystyle \L v_f^2 = v_o^2 + 2g(h_o - h_f)\)

\(\displaystyle \L v_f = \sqrt{v_o^2 + 2g(h_o - h_f)}\)

 

[staceyrho]

What about the angle wouldn't that play a part in the equation?

 

[skeeter]

no. energy is a scalar quantity ... it doesn't care about direction.

 

[staceyrho]

Okay I will try again, I must have miscalculated somewhere.
thanks,