Question

A rocket accelerates from rest at 8.00 m/s^2 for 60.0 s. The engine I'd then shut off. What is the rockets maximum height?

Answer 1

It is supposed to say is not I'd.

Answer 2

Height achieved by Rocket in first 60 s will be given by
\[h_{1} = \frac{ 1 }{ 2 }a.t^{2} = \frac{ 1 }{ 2 }\times8\times(60)^{2} = 14400 m\]
in 60 s it will achieve a speed of 60 *8 = 480 m/s, and now it will moves against gravity so experience a acceleration of 9.8 m/s^{2} opposite to direction of motion.
So on it will moves up until its speed reduces to zero so using third equation of motion
\[h_{2} = \frac{ -(480 m/s)^{2} }{ 2\times(-9.8 m/s^{2}) } = 11755 m\]
Maximum height achieved will be
\[H_{\max} = h_{1}+h_{2} = 14400 m + 11755 m = 26155 m = 26.155 km\]

Answer 3

Thanks