A model rocket with a mass of 2.7kg is launched straight up from the ground at a speed of 110m/s. What is its mechanical energy at the maximum height?

Nov 14, 2015

I found: $16335 J$

Explanation:

At maximum height velocity will be zero so Kinetic Energy will also be zero. Mechanical Energy will be given entirely by Gravitational Potential Energy $U = m g h$.

To find $h$ we use the relationship:

${v}_{f}^{2} = {v}_{i}^{2} + 2 a h$

where:
${v}_{f} =$ final velocity$= 0$;
${v}_{i} =$ initial velocity $= 110 \frac{m}{s}$;
$a = - g$ acceleration of gravity $= - 9.8 \frac{m}{s} ^ 2$ negative because directed downwards;

So:
${110}^{2} = {0}^{2} - 2 \cdot 9.8 h$
$h = 617 m$
And:
$U = 2.7 \cdot 9.8 \cdot 617 = 16335 J \approx 16 K J$