A target glider, whose mass m2 is 390 g , is at rest on an air track, a distance

Question

A target glider, whose mass m2 is 390 g, is at rest on an air track, a distance d = 53 cm from the end of the track. A projectile glider, whose mass m1 is 590 g, approaches the target glider with velocity v1i = -75 cm/s and collides elastically with it (see the figure). The target glider rebounds elastically from a short spring at the end of the track and meets the projectile glider for a second time.

How far from the end of the track does this second collision occur ( cm)?

How long does the target glider take to reach the end of the track?
5.87×10-1 s

How much more time elapses before the gliders collide again?

Explanation / Answer

the distance is calculated as follows:

x = [m1+m2/3m1-m2]d = [590+390 /3*590-390]*53 =37.64 cm

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the final speed: v1f=(m1-m2)/(m1+m2)*v1 = 15.3 cm/s

the final speed: v2f = 2m1/(m1+m2)*v1= 90.3 cm/s

target glider take to reach the end of the track is,

t = 53/90.3 = 0.587 s

time elapses before the gliders collide again is,

t' = (53-37.64)/15.3= 1.004 s

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