math question - How do you solve this problem?

Question

A high jumper falling at 3.9 m/s, lands on a foam pit and comes to rest, compressing the pit a distance of 0.43 m. If the pit is able to exert an average force of -1100 N on the high jumper in breaking the fall, what is the jumper's mass? Thanks for your help...I really want to learn.

Answer 1

The kinetic enegy is removed by the foam:

1/2 m v^2 = force x distance

1/2 m (3.9)^2 = 0.43 x 1100

m = (2 x 0.43 x 1100) / 3.9^2
= 62.2 kg

Answer 2

The change of kinetic energy equals to the work done by the foam.

0 - (1/2)m(3.9 m/s)^2 = (-1100N)(0.43 m)

m = 62.2 kg

Answer 3

Equate the work done by the foam to the kinetic energy of the faller.

work is force x distance

KE = mv^2/2

You have everthing you need to solve for m.

Answer 4

force = Mass * aceleration

let m = the unkown mass

3.9m = -1100
/3.9 = /3.9

m = -282

Answer 5

Using Force:

a = (v_f-v_i)/t
a = (0-3.9)/t
a = -3.9/t
t = -3.9/a

d = v_i*t + 0.5*a*t^2
0.43 = 3.9*(-3.9/a) + 0.5*a*(-3.9/a)^2
0.43 = -15.21/a + 7.605/a
0.43*a = -15.21+7.605
a = -17.69

F = m*a
-1100 = m*-17.69
m = -1100/-17.69
m = 62.2 kg

Or using conservation of energy:

F*d = KE = 0.5*m*v^2
1100*0.43 = 0.5*m*3.9^2
m = 62.2 kg

Answer 6

2.002