How long will it take them to glide to the edge of the rink?

Question

At the center of a 50-diameter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds onto a 60 kg skater who had been heading west at 3.5 m/s.a) How long will it take them to glide to the edge of the rink?b) Where will they reach the edge of the rink? Give your answer as an angle north of west.

Mr. Durward Cummerata · Accepted Answer

a)Conservation of momentum will tell you their resulting speed. Then use that speed to calculate the amount of time it takes to get to the edge.Let:m1=60,m2=75,v1=3.5,v2=2.5, Vx=speed in x direction, Vy=speed in y direction, V=total speedm1*v1=(m1+m2)Vxm2*v2=(m1+m2)VySolve for Vx and Vy and compute. Then compute V=(Vx^2 + Vy^2)^(1/2) r=V*t => t=r/V where r=radius=d/2, d=diameter given as 50 m.b) tan(theta) = Vx/Vy => theta=arctan(Vx/Vy)

Mr. Durward Cummerata · Answer

Let V be the magnitude of the joint velocity. We have V = [√{(752.5)² + (603.5)²}/(75+60)] = [281.5/135] = 2.085 m/sa)Required time = (25/2.085) = 11.988 or 12 sb)Required θ is given by = arctan[(75*2.5)/(60*3.5)] = 41.76° north of west

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How long will it take them to glide to the edge of the rink?

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