Question

A ball is thrown from a height of 49 meters with an initial downward velocity of 2m/s. the ball's height h (in meters) after t seconds is given by the following. h=49-2t-5t² how long after the ball is thrown does it hit the ground?

Answer 1

The ball hits the ground 3.79 seconds after being thrown when we solve the quadratic equation for when the height becomes zero.

Step-by-step explanation:

To determine how long after the ball is thrown it hits the ground, we need to find when the height h is equal to zero in the quadratic equation h = 49 - 2t - 5t². Setting h to zero, the resulting quadratic equation is 0 = 49 - 2t - 5t². To solve this equation, we can use the quadratic formula, which yields two possible solutions for t: t = 3.79 s and t = 0.54 s.

Since the ball is thrown from a height and the initial velocity is downward, it will not go any higher, so the ground is reached on the first occasion the height becomes zero after being thrown. Therefore, we take the positive larger value of time, t = 3.79 s, as the time it takes for the ball to hit the ground.