Question

1a) Marty McFly needs to go 88 mph (39.3 m/s) to jump back to the future. He is riding his hoverboard holding onto the side of a very very short train, which is chugging faster and faster toward the edge of a cliff (on a flat horizontal). If the cliff is 24 m tall and the train hits the ground 95 m from the base of the cliff, did Marty make it back to the future (how fast was the train going horizontally the moment it left the cliff?)?

1b) Is it possible that Marty’s SPEED increased AFTER the train left the tracks and went over the cliff? Explain. Bonus: What THEOREM might you use to figure out his SPEED right before he hit the ground? (Or explain how you would find his final speed)

1c) Could the horizontal component of his velocity have increased during the fall?

Please write it clearly and label the answers

Answer 1

1a)

let us consider that the train hits the ground t secs after jumping from the cliff

here the initial vertical speed Uy=0 and the acceleration is the gravitational acceleration g hence we can write,

h is the height of the cliff h=24

as the train loses its contact with the tracks its accleration becomes 0 and it goes forward with a constant horizental speed(  Vx ,say) and travells 2.21s in air and lands 95m from the base of the cliff.hence,

hence since his speed exceeds 39.3m/s hence he is able to travell to future

b)

after it left the tracks there is a vertical component of speed (t=time ) that adds with the horizental component as a result the magnetude of speed increases

to find its final speed we have to use the law of conservation of energy

here Vfinal is the speed of the train after landing , Vinitial is the speed before leaving the cliff and h is the height of the cliff

c) during the fall the horizental component of velocity was constant since there was no horizental accelaration during this time.