A man jumps with a speed v(xi) from a roof at a height of 10m. He falls 3m from the wall. What is its initial velocity v(xi)?

Problem: a man jumps with a speed v(xi) from a roof at a height of 10m. He falls 3m from the wall. What is its initial velocity v(xi)?
1. I first calculate the time from the jump with the formula: y(f)-y(i) = v(yi)t-1/2gt². v(yi) = 0 then t=1.43s.
2. I plug this value into the formula x(f)-x(i)=v(xi)t-1/2(9.81)(1.43)² v(xi) = 9.11 m/s.
My question: is (2) correct?

Asker: Fund, 63 years old

Answer

The fall time is indeed 1.43 seconds.

However, the second part of your solution is wrong because in the x-direction there is no acceleration, because no force, (if we neglect air resistance). The gravitational term with g in it is therefore not present in the x-direction. So there it is basically simpler than what you do:

x

So we fill in : 3 = v(xi) . 1.43

so that v(xi) = 2.10 m/s

A man jumps with a speed v(xi) from a roof at a height of 10m.  He falls 3m from the wall.  What is its initial velocity v(xi)?

Answered by

prof.dr. Paul Hellings

Department of Mathematics, Fac. IIW, KU Leuven

Catholic University of Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/

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