Question 1 A spaceship has a length of 120 meters in its rest frame and it is tr

Question

Question 1

A spaceship has a length of 120 meters in its rest frame and it is traveling at a speed of 0.8c relative to the Earth. Find the following:

Length of the spaceship as seen by an observer on the Earth.

Time elapsed on the spaceship given that 100 minutes have passed on a clock on the Earth.

Question 2

A pi+ meson is a subatomic particle, which has a lifetime of 2.6 * 10 -8seconds. A particle accelerator produces a pi+ meson and it is measured to live for
2.6 * 10-7seconds. Calculate how fast the pi+ meson is moving.

Question 3

A car travels down a 10 km long track. But the track measures 8 km on the car's odometer. To solve this problem, you need to know the speed of light, which is approximately 3 * 108 m/s. Calculate the following:

How long did the car take to travel down the track according to someone standing next to the track?

How long did the car take to travel down the track according to the car's driver?

Explanation / Answer

1. Y = 1 / sqrt[1 - (v/c)^2]

= 1 / sqrt(1 - 0.8^2)

= 1.67

length as seen by oserver L = Lo / Y

= 120 / 1.67

= 72 m ...........Ans

time on spaceship. t0 = t / Y = 100 / 1.67

= 60 minutes. ......Ans

2. Y = 2.6 x 10^-7 / (2.8 x 10^-8) = 10

Y = 1 / sqrt(1 - (v/c)^2) = 10

1 - (v/c)^2 = (1/10)^2

v = 0.995 c

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