Question

# boy has a mass of 55.0kg, is skiing 3.50 m/s west when he runs head on...

boy has a mass of 55.0kg, is skiing 3.50 m/s west when he runs head on into a girl,

mass = 45.0 kg, going east at 2.50 m/s.  To decrease the impact he grabs the girl so they are stuck together. (using calc physics)

What is the total momentum (magnitude and direction) just before the collision?

What is the total momentum (magnitude and direction) right after the collision?

What is the final velocity of the goofy and the girl?

How much kinetic energy is lost in the collision?

let the speed after the collision be V m/s

momentum before collision = m1u1 + m2u2

= 55*3.5 + 45*-2.5

= 80 kg m/s (west)

by the conservation of momentum,

momentum after collision = momentum before collision

momentum after collision = 80 kg m/s (west)

80 = (m1 + m2)V

V = 80 / (55 + 45) = 0.8 m/s to the west

KE(initial) = 0.5m1u1^2 + 0.5m2u2^2

= 0.5*55*3.5^2 + 0.5*45*(-2.5)^2

= 477.5 J

KE(final) = 0.5(m1 + m2)V^2

= 0.5*(55 + 45)*0.8^2

= 32 J

Kinetic energy lost in collision = Initial KE - Final KE

= 477.5 - 32 = 445.5 J

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