Question

Jill claims that her new rocket is $100m$long. As she flies past your house, you measure the rocket’s length and find that it is only $80m$ What is Jill’s speed, as a fraction of $c$?

Short answer

Jill have a speed$0.6c$

Step-by-step solution

Given Information

We have given that the length of the new rocket is $100m$.

We need to find Jill’s speed.

Simply 

Consider:

$$\begin{gathered} L=100m \\ L\text{'}=80m \end{gathered}$$

using formula:

$L\text{'}=L\sqrt{\left(1-\frac{v^2}{c^2}\right)}...\left(1\right)$

Solve $\frac{v}{c}$from equation (1)

$$\begin{gathered} L\text{'}=L\sqrt{\left(1-\frac{v^2}{c2}\right)} \\ \frac{L\text{'}}{L}=\sqrt{\left(1-\frac{v^2}{c2}\right)} \\ \frac{80}{100}=\sqrt{\left(1-\frac{v^2}{c2}\right)} \\ 0.8=\sqrt{\left(1-\frac{v^2}{c2}\right)} \\ 0.64=\left(1-\frac{v^2}{c2}\right) \\ 0.36=\frac{v^2}{c2} \\ 0.6=\frac{v}{c} \\ \Rightarrow v=0.6c \end{gathered}$$

Jill's speed is $0.6c$from speed of light