Question

A man throws a ball into the air with a velocity of 96 ft/s. Use the formula h=−16t+v0t to determine when the height of the ball will be 48 feet. Round to the nearest tenth.

a) 1.5 seconds
b) 2.0 seconds
c) 3.0 seconds
d) 3.5 seconds

Answer 1

Using the formula h = -16t^2 + v0t and setting h to 48 feet and v0 to 96 ft/s, we rearrange the equation and solve the quadratic to find that the ball will be 48 feet in the air at approximately 3.0 seconds, which matches the answer choice (c).

Step-by-step explanation:

To determine when the height of the ball will be 48 feet, the formula h = -16t^2 + v0t can be used, where h is the height after t seconds and v0 is the initial velocity. In this case, h is 48 feet, and v0 is 96 ft/s. Let's set up the equation with the given values:

48 = -16t^2 + 96t

To solve this quadratic equation, we can either factorize, use the quadratic formula, or try possible solutions. Let's start by rearranging:

0 = -16t^2 + 96t - 48

Now, divide all terms by -16 to simplify:

0 = t^2 - 6t + 3

If we solve this quadratic equation, we are likely to find two possible times when the ball is at 48 feet (once on the way up and once on the way down). After calculating, we find that one of the solutions is t = 3.0 seconds, which corresponds to answer choice (c).