Physics question: 1-dimensional collision question...?
A 98.4 kg football halfback carries the ball past the line of scrimmage running at 7.02 m/s north. He is tackled by a linebacker running at 4.76 m/s south. their combined velocity after the 0.285 second collision is 1.02 m/s north.
a. find the impulse received by the halfback,
b.what is the mass of the linebacker?
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a/ Impulse is change in momentum, which is final momentum minus initial momentum. Momentum is mass times velocity.
So we can write impulse = mass times (final velocity minus initial velocity) and if we define northward motion to be the positive direction (and south negative) then
P = 98.4 kg(1.02 m/s - 7.02 m/s)
= -590.4 kg m/s.
b/. Total momentum throughout the collision must be conserved so total momentum after the collision must be equal to total momentum before the collision. After the tackle, we can consider the players to stick together to create an object, if we call the linebacker's mass m, of mass 98.4 + m.
So total momentum after collision = (98.4 + m)1.02
Total momentum before collision = halfback's momentum (98.4 kg)(7.02 m/s) + linebacker's momentum (m)(-4.76 m/s), or
(98.4 + m)1.02 = (98.4)(7.02) - 4.76m
or 100.368 + 1.02m = 690.768 - 4.76 m
or 5.78 m = 590.4, or
m = 102.1 kg.
Find the momentum vectors. Calculate the x and y accessories of each. Then calculate the ultimate x and y momentum vectors. To find the ensuing, then divide by using mass to get speed.