need help with this question, all parts A young boy called Nick is stranded at t

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need help with this question, all parts

A young boy called Nick is stranded at the airport with his father, Tom, because of bad weather. To pass the time, they decide to have a race. The race is an out-and-back race, starting and ending at the same place. Tom runs at constant speed a distance L, and then turns around and comes back. Nick, because he is so young, gets an advantage: while running away from the start line, he runs on a moving sidewalk, of length L, that is traveling in the same direction he is going. At the end of the moving sidewalk, he turns and runs back on the non-moving floor. In other words, he only runs on the moving sidewalk in one direction. Tom's constant speed is 6.00 m/s. Nick runs at a speed v with respect to the moving sidewalk, and with respect to the non-moving floor on the way back. The moving sidewalk's speed, with respect to the floor, also happens to be v. (a) Tom and Nick start at the same time, and the race ends in a tie. Calculate the value of v. (b) Because Nick starts on the moving sidewalk, he is ahead of Tom the whole time, until they reach the finish line. What is the largest distance separating Nick and Tom during the race? The largest distance measured parallel to the race course, of course. To answer this, you need the value of L, which is 42.0 m. (c) At some distance from the start line, Tom and Nick pass one another - Tom is still running away from the start line at this point, while Nick is on his way back. How far is this point from the start line? (d) It turns out that Usain Bolt is also in the airport, and he sees the race. He then challenges Nick and Tom to race against him. Nick and Tom will do exactly what they did before, while Bolt runs on the non-moving floor for the first part of the race, and then turns around and runs back on the moving sidewalk (the same one Nick runs on), which is traveling opposite to the way Bolt is running on it. Bolt runs at the same speed relative to the moving sidewalk that he does on the floor. For Bolt to tie Nick and Tom, what would his speed (relative to the moving sidewalk) have to be?

Explanation / Answer

a)

time taken by tom = time taken by nick

2L/6 = L/(v + v) + L/v

1/3 = 1/(2v) + 1/v

v = 4.5 m/s

b)

tn = time taken by nick to travel length "L" = L/2v = 42/(2 x 4.5) = 42/9

d = distance travelled by tom in time "tn" = 6 tn = 6 (42/9) = 28 m

so maximum distance = 42 - 28 = 14 m

c)

t = time taken by nick to meet tom while returning after time "tn" = 14/(6 + v) = 14/10.5 =

D = distance from start line = (tn + t) 6 = ((42/9) + (14/10.5)) (6) = 36 m

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