Question

If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, how long will it take the baseball to hit the ground? Use the equation h = −16t2 + 4t + 4. Round your answer to the nearest hundredth.

Answer 1

0.64 seconds

Explanation:

In the equation provided:

h = −16t2 + 4t + 4

h is the height of the ball and t is time. Since we want to find the time when the ball touches the floor, then height is 0. This leaves us with the equation

-16
`t^(2)` + 4t + 4 = 0

This is a quadratic equation can be solved with the following formula:

`x= \frac{-b+-\sqrt{b^(2)-4ac } }{2a}`

where a=-16

b=4

c=4

Solving for t we will find two different results:

`t1=(-4-√(272) )/(2(-16)) =0.125+0.125√(17) =0.64039`
`t2=(-4+√(272) )/(2(-16)) =0.125-0.125√(17) =-0.39039`

Since time can't be negative, we discard t2 and choose t1.

Since it is required to answer in the nearest hundredth, we round the result to t=0.64 seconds.