Two people are sitting on playground swings. One is pulled back 4 degrees from the vertical and the other is pulled back 8 degrees. They are both released at the same instant. Will they both come back to their starting points at the same time

The bodies will not come back to their starting point at he same time.

Explanation:

Since they are both pulled back at an angle to the vertical, there is a tangential component of acceleration a = gsinθ

When θ = 4 , a = 9.8sin4 = 0.684 m/s²

When θ = 8 , a = 9.8sin8 = 1.364 m/s²

Using s = ut + 1/2at². Where s is the distance covered and t = time taken, u = initial speed = 0 (assumed since they are both released at the same time)

So s = 0 × t + 1/2at² = 1/2at²

s = 1/2at²

t = √2s/a. Now, since s is the same for both swings, it follows that

t ∝ 1/a. Since their accelerations are different, the bodies will not come back to their starting point at he same time.

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