PROBLEM 5Imagine that a man is running at his top speed v to catch a bus that is stopped at a traffic light. When he is still adistance d from the bus, the light changes and the bus starts to move away from the running man with aconstant acceleration a. When will the man catch the bus? Explain your answer.This is the distance travelled by the bus = dAliosof theSpeed of the personThe total distance travelled by a man to catch the bus = d+ d.consider man:Given:x, =d+d, distance travelled by the manconsider man:d = distance of the man to the busx, =v•d+d, = v•, → eq. 1before the bus start to moveconsider bus:v = velocity of the mant = time of mand, = v1+-a ·1, distance travelled by the busconsider bus:1,= time of the bus=a-t → cq. 2d, = distance travelled by the bussubstitute eq.2 to eq.1Vi = 0 velocity initial of the busa = acceleration of the busd+a•1, =v•t, , =1,note: time of the man is same of the busd+Reg:t =? time to catch the bus++d =0[ 22v±2,(v – 2ada t - 2v·1+2d = 02ause quadratic eq. to solve for t.vt(v - 2ad)ax? + bx +c = 02aa = ab = -2vc = 2dFrom here, we are only concern about-bt Vb? - 4acthe nature of the discriminant. If it is2aimaginary.v2 - 2ad → should not be less than zeroor else we will have an imaginary value.real-(-2v)± (-2v)² – 4(a)(2d)2(a)2vtV4v - 8ad2aThus, we can conclude that the man can catch the bus2v± 4(v² – 2ad)only if he will be able to attain a speed which will be2aequal to or higher that the value of sqrt(2ad).14Science is the belief in the ignorance of experts – Richard Feynman

Name: PROBLEM 5Imagine that a man is running at his top speed v to catch a
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: PROBLEM 5Imagine that a man is running at his top speed v to catch a bus that is stopped at a traffic light. When he is still adistance d from the bus, the light changes and the bus starts to move away from the running man with aconstant acceleratio