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?

Question

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?

Answer 1

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

start with momentum conservation:

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

Answer 2

To determine the mass of the football player, we need to apply the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is defined as the product of its mass and velocity: momentum = mass × velocity.

Let's denote the mass of the football player as "m1" and the mass of the referee as "m2." According to the given information, we know:

m1 × velocity1 = m2 × velocity2

where:
- velocity1 is the initial velocity of the football player (8 m/s)
- velocity2 is the final velocity of the referee after the collision (5 m/s)
- m1 is the mass of the football player (what we want to find)
- m2 is the mass of the referee (80 kg)

Now, we can plug in the values into the equation:

m1 × 8 m/s = 80 kg × 5 m/s

Simplifying the equation:

8 m1 = 400 kg m/s

Dividing both sides by 8:

m1 = 50 kg

Therefore, the mass of the football player is 50 kg.

Answer 3

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

Answer 4

Such collisions are not elastic.

Are you sure they are not asking about an inelastic collision?