# 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?

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

#### 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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