Marty McFly needs to go 88 mph (39.3 m/s) to jump back to the future. He is ridi

Question

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?)?

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)

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

Explanation / Answer

SOLTION

Let the train hit the ground after time t after leaving the cliff.

While falling from 24 m high cliff,

24 = (1/2)gt2    ............................1)

Let the horizontal velocity be u,

Then,     u = 95/t

or ,    t = 95/u   ..............................2)

from 1) and 2)

24 = (1/2)g*(95/u)2

or,      u2 = 952*0.5*9.81/24

or,     u = 43 m/s

As u>39.3 m/s , Marty made it back to the future.

Marty's horizontal speed reamins same, u = 43 m/s

Marty's vertical speed on hitting the ground, v = g*t = 9.81*95/43 = 21.7 m/s

Marty's final speed, V = (v2+u2)1/2 = 48.16 m/s

No, horizontal component of his velocity could not have increased during the fall.

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