In this problem, we'll use the kinematic equations:

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathit{a}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{+}}{\frac{1}{2}}{\mathit{a}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathit{a}}{\mathbf{\u2206}}{\mathit{x}}}$

The maximum height reached:

$\overline{){{\mathbf{h}}}_{\mathbf{m}\mathbf{a}\mathbf{x}}{\mathbf{=}}\frac{{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}}{\mathbf{2}\mathbf{g}}}$

**a.**

The velocity of the rocket when teh engine fails can be found from the kinematic equation:

v_{f}^{2} = v_{0}^{2} + 2aΔx

$\begin{array}{rcl}{{\mathbf{v}}_{\mathbf{f}}}^{\mathbf{2}}\mathbf{-}{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}& \mathbf{=}& \mathbf{2}\mathbf{a}\mathbf{H}\\ {{\mathbf{v}}_{\mathbf{f}}}^{\mathbf{2}}\mathbf{-}\mathbf{0}& \mathbf{=}& \mathbf{2}\mathbf{a}\mathbf{H}\\ {\mathbf{v}}_{\mathbf{f}}& \mathbf{=}& \sqrt{\mathbf{2}\mathbf{a}\mathbf{H}}\\ & \mathbf{=}& \sqrt{\mathbf{\left(}\mathbf{2}\mathbf{\right)}\mathbf{(}\mathbf{2}\mathbf{.}\mathbf{30}\mathbf{)}\mathbf{\left(}\mathbf{555}\mathbf{\right)}}\end{array}$

v_{f} = 50.527 m/s

The motion between the interval 555 m and h_{max}:

A 7550 kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.30 m/s^{2} and feels no appreciable air resistance. When it has reached a height of 555 m, its engines suddenly fail so that the only force acting on it is now gravity.

You may want to review (Pages 50 - 53).

For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Up-and-down motion in free fall.

a. What is the maximum height this rocket will reach above the launch pad?

b. How much time after engine failure will elapse before the rocket comes crashing down to the launch pad?

c. How fast will it be moving just before it crashes?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Vertical Motion and Free Fall concept. You can view video lessons to learn Vertical Motion and Free Fall. Or if you need more Vertical Motion and Free Fall practice, you can also practice Vertical Motion and Free Fall practice problems.