# physics

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a football player runs at 8 m/s and plows into a 80 kg referee standing on the field causing the referee to fly forward at 5 m/s. if this were a perfectly elastic collision, what would the mass of the football player be?

• physics -

Such collisions are not elastic.

• physics -

thats the exact question. I am trying to help my daughter, her answer does not seem right to me she got 100 kg. Do you know how to solve this problem step by step. ty

• physics -

36.4

• paragon -

I will give you an outline of the derivation:

call v0 the speed of the first ball before collision, v1 and v2 the speeds of the first and second balls after collision

m1, m2 are the masses of the first and second balls

m1 v0 = m1 v1 + m2 v2

rewrite as m2 v2 = m1(v0-v1)

energy conservation gives you

1/2 m 1 v0^2 = 1/2 m1 v1^2 + 1/2 m2 v2^2

divide through by 1/2 and rewrite:

m2 v2^2 = m1(v0^2-v1^2) = m1 (v0-v1)(v0+v1)

but from momentum we know that m2 v2 = m1(v0-v1), so substitute this into the energy equation and get

m2 v2^2 = m2 v2 (v0+v1) or v2 = v0+v1

substitute this back into the momentum equation and get that

v1 = (m1-m2)v0/(m1+m2)

which then yields

v2 = 2 m1 v0/(m1+m2)

in this case, v0=8m/s, m2 = 80kg, and v2=5m/s and we want to find m1

we have (using the v2 equation):

5m/s = 2 m1 x 8m/s/(80+m1)

solving for m1:

400 + 5m1 = 16m1

400 = 11m1

m1 = 36.4kg