Q77P - University Physics with Modern Physics

Question

During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth’s surface and is to reach a maximum height of 960 m above the earth’s surface. The rocket’s engines give the rocket an upward acceleration of 16.0 m/s2 during the time T that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance. What must be the value of T in order for the rocket to reach the required altitude?

Step-by-Step Solution

Answer

The value of T is 15.49 s.

Step1: Identification of given data

Maximum height = 960 m

Upward acceleration = 16.0 m/s²

Step1: Calculation for the time T

As we know that

$$\begin{gathered} \mathrm{d}=\frac{1}{2}\times {\mathrm{aT}}^2 \\ 960=\frac{1}{1}\times 16.0\times {\mathrm{T}}^2 \\ \mathrm{T}=15.49\mathrm{s} \end{gathered}$$