Ben and Jack are shopping in a d inclined at an angle of 36° above the horizonta

Question

Ben and Jack are shopping in a d inclined at an angle of 36° above the horizontal, and travels eastward and upward at the speed of 2.0 m/s store. Ben leaves Jack at the bottom of the escalator and walks east at a speed of 2.09 m/s. Jack gets on the escalator, which is (a) What is the velocity of Ben relative to Jack? magnitude direction m/s o below the horizontal (b) At what speed should Jack walk, relative to the escalator, so that he is always directly above Ben (until he reaches the top)? m/s

Explanation / Answer

Ben velocity = 2.09 m/s (east)

Jack speed = 2 m/s (East-Up)

incline makes 30 deg

Jack velcoity along the horizontal (east) = 2Cos(30) = 1.73 m/s (east)

                                  Up                          = 2sin(30)     = 1 m/s (up)

Ben vel. relative to Jack     = 2.09 - 1.73 = 0.36 m/s (east)

b) For jack to be always above Ben, his horizontal vel. has to be same aas that of Ben

               vCos(30) = 2.09 m/s

               v = 2.41 m/s

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