Catherine Green
Dec 21, 2024
How long will it take them to glide to the edge of the rink?
At the center of a circular ice rink with a diameter of 50 meters, a 75 kg skater is moving north at a speed of 2.5 m/s when they collide with and hold onto a 60 kg skater who was traveling west at 3.5 m/s.
a) How long will it take for them to glide to the edge of the rink?
b) At what angle relative to west (north of west) will they reach the edge of the rink? Please provide your answers with clear reasoning.
2 Answers
Nov 22, 2024
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)
Dec 21, 2024
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
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