Answer to Question #164143 in Mechanics | Relativity for Bert

Question

A woman on the earth firecracker explode 10.0m in front of her when her clock reaches 5.0 seconds an astronaut in rocketship who passes the woman on earh at t=0 at speed of 0.40c. Find what coordinate for this event?

Answer 1

Explanations & Calculations

• Since the rocket is flying with relativistic speed, the time taken for the firecracker to explode is detected differently by the women and the astronaut.
• This phenomenon is described by the equation,

$\qquad\qquad \begin{aligned} \small T&= \small \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\cdot\tau \end{aligned}$

where T represents the time seen by the earth bounder & $\tau$ represents time seen by the one in the reference frame moving at relativistic speed.

• Therefore,

$\qquad\qquad \begin{aligned} \small 5\,s &= \small \frac{1}{\sqrt{1-0.4^2}}\cdot\tau\\ \small \tau &= \small 5\times 0.916515139\\ &= \small 4.583\,s \end{aligned}$

• The astronaut sees the cracker explode after 4.583 s after he passes the women