Question

A baseball is thrown vertically upward at a rate of 65 feet per second from an initial height of 4 feet. Use the projectile formula h = − 16 t 2 + v 0 t + h 0. determine when the ball will hit the ground. [recall that v 0 is the initial velocity of the object and h 0 is the inital height of the object.]

Answer 1

To determine when the ball will hit the ground, we can use the projectile formula and solve a quadratic equation to find the time. The ball will hit the ground approximately 0.718 seconds after being thrown.

Step-by-step explanation:

To determine when the ball will hit the ground, we need to find the time it takes for the ball to reach a height of 0 feet. We can use the projectile formula h = -16t^2 + v0t + h0, where h is the height, t is the time, v0 is the initial velocity, and h0 is the initial height. In this case, the initial height h0 is 4 feet, so the equation becomes 0 = -16t^2 + 65t + 4. We can solve this quadratic equation to find the time t when the ball hits the ground.

Using the quadratic formula, t = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = -16, b = 65, and c = 4. Plugging in these values, we get t ≈ 0.718 seconds or t ≈ 4.781 seconds. Since we're looking for the time when the ball hits the ground, we discard the second solution. Therefore, the ball will hit the ground approximately 0.718 seconds after being thrown.