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.
2 Answers
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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 speed
m1*v1=(m1+m2)Vx
m2*v2=(m1+m2)Vy
Solve 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)
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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/s
a)Required time = (25/2.085) = 11.988 or 12 s
b)Required θ is given by = arctan[(75*2.5)/(60*3.5)] = 41.76° north of west
