   Chapter 6, Problem 30P

Chapter
Section
Textbook Problem

Three ice skaters meet at the center of a rink and each stands at rest facing the center, within arm’s reach of the other two. On a signal, each skater pushes himself away from the other two across the frictionless ice. After the push, skater A with mass mA = 80.0 kg moves in the negative y-direction at 3.50 m/s and skater B with mass mB = 75.0 kg moves in the negative x-direction at 4.00 m/s. Find the x- and y-components of the 90.0-kg skater C's velocity after the push.

To determine
Velocity of x- and y- component of the skater “C”.

Explanation

Given Info: Mass of the skater A is mA=80.0 kg , mass of the skater B is mB=75.0 kg , mass of the skater C is mC=90.0 kg , velocity of skater A in negative y- direction is vA=3.50 m/s , velocity of skater B in negative x- direction is vB=4.00 m/s and Initial velocities of the skaters are zero

Explanation:

Apply conservation of momentum.

pi,x =pf,xpi,y=pf,y (1)

• pi,x is the initial x component of momentum
• pf,x is the final  x component of momentum
• pi,y is the initial y component of momentum
• pf,y is the final y component of momentum

Rewrite equation (1) in terms of mass and velocity along with zero for initial velocities.

mBvB+mcvx=0vx=mBvBmc (2)

• vB is the velocity of the skater B.
• mB is the mass of the skater B.
• mc is the mass of the skater C.
• vx is the velocity of the x component.

Similarly for the momentum due to y axis

mAvA+mcvy=0vy=mAvAmcm/s (3)

• vA is the velocity of the skater A

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