Question

If an object is dropped from a height of 400 feet, the function h(t)= -16t^2+400 gives the height of the object after t seconds. When will the object hit the ground? A. 5 s B. 2.5 s C. 10 s D. 25 s

Answer 1

To find out when the object will hit the ground using the function h(t) = -16t^2 + 400, set h(t) to 0 and solve for t. The solution is t = 5 seconds, meaning the object will hit the ground after 5 seconds.

Step-by-step explanation:

To determine when the object will hit the ground using the function h(t) = -16t^2 + 400, we need to solve the equation for when h(t) equals zero since the height of the object will be 0 when it touches the ground. Setting the function equal to 0 and factoring yields:

0 = -16t^2 + 400.

To solve for t, we divide both sides by -16, which simplifies the equation to:

t^2 = 25.

By taking the square root of both sides, we find that t = 5 seconds, as negative time would not make sense in this context. Therefore, the object will hit the ground after 5 seconds.