You toss a polybutadiene rubber ball 40 feet straight up from ground level. Each time it bounces, it rebounds 2/3 of the distance from which it fell. It continues bouncing indefinitely. How far does it travel before it comes to rest?

40 feet.

trick answer! Nice one.

To find out how far the polybutadiene rubber ball travels before coming to rest, we need to sum the distance covered during each bounce.

The ball is initially thrown 40 feet straight up from ground level. When it first falls back to the ground, it covers a distance of 40 feet before bouncing up.

During the first bounce, the ball rebounds 2/3 of the distance from which it fell, which is (2/3) * 40 = 80/3 feet.

For subsequent bounces, the ball's distance covered will keep getting smaller, as it rebounds 2/3 of the previous distance each time.

Therefore, the total distance traveled is the sum of the distance during each bounce:

40 + (80/3) + (80/3) * (2/3) + (80/3) * (2/3)^2 + ...

This is an infinite geometric series with a first term (a) of 40 and a common ratio (r) of 2/3 (as the ball rebounds 2/3 of the distance each time).

To find the sum of an infinite geometric series, we use the formula: S = a / (1 - r), where S represents the sum.

Plugging in the values, we have:

S = 40 / (1 - 2/3)
S = 40 / (1/3)
S = 120 feet

Therefore, the ball travels a total distance of 120 feet before coming to rest.