The net is 3 feet high. The distance from where the ball is hit to the net is 24 feet. Assume the ball travels in a straight line. At what height must a tennis ball be hit so that it will just pass over the net and land 21 feet away from the net on the other side?
To find the height at which the tennis ball must be hit, we can use the concept of similar triangles.
Let's break down the problem:
1. The net is 3 feet high.
2. The distance from where the ball is hit to the net is 24 feet.
3. The ball must pass over the net and land 21 feet away from the net on the other side.
To find the height at which the tennis ball must be hit, we can set up a proportion:
(height of ball) / (dist from hit to net) = (height of net) / (distance from net to landing spot)
Let's substitute the given values into the proportion:
(height of ball) / 24 = 3 / 21
To solve for the height of the ball, we need to cross-multiply and then solve the equation:
(height of ball) * 21 = 24 * 3
(height of ball) * 21 = 72
Now we can isolate the height of the ball by dividing both sides of the equation by 21:
(height of ball) = 72 / 21
Calculating this, we find that the height of the ball must be approximately 3.43 feet.
Therefore, the tennis ball must be hit at a height of approximately 3.43 feet to clear the net and land 21 feet away from it on the other side.