Two rugby players collide on a field. Player 1 has a mass of 100 kg. Player 2 ha

Question

Two rugby players collide on a field. Player 1 has a mass of 100 kg. Player 2 has a mass of 90 kg. Player 1 has a velocity of 10 m/s in the +x direction. Player 2 has a velocity of 6 m/s in the +y direction.

a.What is the magnitude of the velocity of the 2 players moving together immediately after the collision? Assume a perfectly inelastic collision. Please report your answer in units of m/s^2.

b.What is the direction of the velocity for the 2 players from the x-axis? Please report your answer in units of degrees.

Explanation / Answer

Let m1 = 100Kg, m2 = 90Kg, u1 = 10i m/s u2 = 6j m/s Let v be their final velocity moving together.

Let v = xi+yj

Then, by conservation of momentum,

m1u1+m2u2 = (m1+m2)v

100*10i+90*6j = 190(xi+yj)

1000i+540j = 190(xi+yj)

Comparing both sides, we see, 190x = 1000 => x = 5.26 and 190y = 540 => y = 2.84

Hence magnitude of v = sqrt[(5.26)^2+(2.84)^2] = sqrt(27.67+ 8.07) = 5.98m/s

Direction is tanA = -y/x = -2.84/5.26 = -0.54

=> A = -28 degrees or 360-28 = 332 degrees from +x axis.

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