You and your friends just finished watching Back To The Future and---feeling a b

Question

You and your friends just finished watching Back To The Future and---feeling a bit of a binge coming on---decide to watch the sequel, Back To The Future II. During one famous scene, Marty is trying to escape getting pummeled by a group of bullies. He borrows a young girl's hoverboard and jumps on. You're curious as to whether Marty would be moving faster or slower after jumping on the hoverboard, so you decide to work out what Marty's speed would be before he landed on the board. You assume that Marty is about 70 kg and that the hoverboard is itself about 5 kg and that they move straight along the ground together with a speed of about 10 mph.

Explanation / Answer

m = 5kg

M = 70 kg

speed after landing, v = 10 mph

Let the speed of Marty before landing be u

So, initial momentum of Marty = M*u

final momentum of the board and Marty after landing on the board, = (m+M)*v

By conservation of momentum, initial and final momenta must be same

So, Mu = (m+M)*v

So, u = ((m+M)/M)*v = ((5+70)/70)*10 = 10.7 mph <----------answer

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