### 41 a star is moving toward the earth with a speed of 0 9 c 90 the speed of light it 4294833

41) A star is moving toward the Earth with a speed of 0.9 *c* (90% the speed of light). It emits light, which moves away from the star at the speed of light. Relative to us on Earth, the speed of the light moving towards us (emitted by the star) is

A) c

B) 1.9 c

C) 1.2 c

D) 0.98 c

42) A spaceship is moving in a straight line at a speed of 0.8 *c* (relative to Earth). It launches a missile that moves away from the spaceship (traveling in the same direction as the spaceship) at a speed of 0.6 *c*. Relative to Earth, the speed of the missile is

A) greater than 0.8 *c* and less than *c*.

B) 1.4 *c*.

C) *c*.

D) greater than *c* and less than 1.4 *c*.

43) The kinetic energy of an object moving at 10% the speed of light is

A) slightly higher than that given by (1/2) *m v**2.*

B) slightly less than that given by (1/2) *m v**2.*

C) exactly equal to (1/2) *m v**2.*

**Short Answer Questions**

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1) An unstable particle is moving at a speed of 1.6 *×* 108 m/s relative to a laboratory. Its lifetime is measured by a stationary observer in the laboratory to be 6.8 *×* 10-6 seconds. What is the lifetime of the particle, measured in the rest frame of the particle? (Use 3.00 *×* 108 m/s for the speed of light.)

2) A spacecraft is measured by an observer on the ground to have a length of 81 m as it flies overhead with a speed 2.4 *×* 108 m/s. The spacecraft then lands and its length is again measured by the observer on the ground, this time while the spacecraft is at rest relative to him. What result does he now get for the length? (Use 3.00 *×* 108 m/s for the speed of light.)

3) How much work must be done to accelerate a particle of mass 3.5 *×* 10-14 kg (rest mass) from a speed of 1.2 *×* 108 m/s to a speed of 1.9 *×* 108 m/s? (Use c = 3.00 *×* 108 m/s for the speed of light.)

4) Two spaceships are approaching one another, each at a speed of 0.31 c relative to a stationary observer on earth. What speed does an observer on one spaceship record for the other approaching spaceship?

5) A 50.0 kg object is pushed in the direction it is moving by a 100.0 N force. Find the acceleration this force produces if the object has a speed of (a) 25.0 m/s, (b) 2.50 × 108 m/s. (c) In parts (a) and (b), find the momentum of the object.