An arrow is 1.10 m long when at rest. A target is located 30.0 m away from Bob.

Question

An arrow is 1.10 m long when at rest. A target is located 30.0 m away from Bob. Bob shoots the arrow toward the target, the arrow moves at 92.0% the speed of light. Spot, the ladybug, is holding onto the arrow as it is flying. We need to know the following during the flight of the arrow:

(a) How long does Bob think the arrow is

(b) How long does Spot think the arrow is

c) How far does Spot think the target is at time t = 0?

d) How long (time) does Bob think that the arrow takes to go from bow to target?

e) How long (time) does Spot think that the target takes to approach the arrow

Explanation / Answer

(a) How long does Bob think the arrow is

LB = L0/gamma , here gamma(g) = 1/(1-(v2/c2))1/2  

so , LB = 1.10*(1-(v2/c2))1/2 = 1.10(1-((0.92c)2/c2))1/2 = 1.1* 0.392 = 0.4312 metre

(b) How long does Spot think the arrow is

L0 = 1.1 m

c) How far does Spot think the target is at time t = 0?

d) How long (time) does Bob think that the arrow takes to go from bow to target?

e) How long (time) does Spot think that the target takes to approach the arrow

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