Final answer:
The function that gives the height of a bowling ball dropped from a height of 24 feet is -16t^2 + 24. After 1 second, the height of the ball is 8 feet. It takes about 1.5 seconds for the ball to hit the ground.
Step-by-step explanation:
a. To find the function that gives the height h (in feet) of the bowling ball after t seconds, we can use the equation h(t) = -16t^2 + h0, where h0 is the initial height. In this case, the initial height is 24 feet, so the function becomes h(t) = -16t^2 + 24.
b. To find the height of the bowling ball after 1 second, we can substitute t = 1 into the function. h(1) = -16(1)^2 + 24 = -16 + 24 = 8 feet.
c. To find how long it takes for the bowling ball to hit the ground, we need to set the function h(t) equal to 0 and solve for t. -16t^2 + 24 = 0. Solving this equation gives us two solutions, t = 1.5 seconds and t = -1.5 seconds. Since time cannot be negative in this context, the bowling ball takes about 1.5 seconds to hit the ground.