Question

A baseball will reach height h feet after t seconds, as estimated by the formula

h(t) = 2 + 90t - 16t^2
At what time(s) will the baseball be 76 feet high? (Explain how you got the answer/show work in the space provided)

Answer 1

`t = 1,(37)/(8) \text{ sec}`

Explanation:

We are given the equation h(t) i.e. height h feet in time t:

`h(t) = 2 + 90t - 16t^2`

We are given that value of h(t) is 76 feet and have to find the value of t.

`\Rightarrow 76=2 + 90t - 16t^2\\\Rightarrow 74= 90t - 16t^2\\\Rightarrow 16t^2 -90t +74=0\\\Rightarrow 8t^2 -45t +37=0\\`

Using factorization method to solve the above quadratic equation:

We know that 45t = 8t + 37t :

`\Rightarrow 8t^2 - 8t - 37t +37 =0\\\Rightarrow 8t(t - 1) - 37(t -1) =0\\\Rightarrow (t - 1)(8t - 37) =0\\\Rightarrow t =1 \text { or } (37)/(8)`

At time ,
`\text{t = 1 sec or }(37)/(8) \text{ sec}` , the height of baseball will be 76 feet.