Answer:
[tex]t = 1,\dfrac{37}{8} \text{ sec}[/tex]
Step-by-step explanation:
We are given the equation h(t) i.e. height h feet in time t:
[tex]h(t) = 2 + 90t - 16t^2[/tex]
We are given that value of h(t) is 76 feet and have to find the value of t.
[tex]\Rightarrow 76=2 + 90t - 16t^2\\\Rightarrow 74= 90t - 16t^2\\\Rightarrow 16t^2 -90t +74=0\\\Rightarrow 8t^2 -45t +37=0\\[/tex]
Using factorization method to solve the above quadratic equation:
We know that 45t = 8t + 37t :
[tex]\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 } \dfrac{37}{8}[/tex]
At time , [tex]\text{t = 1 sec or }\frac{37}{8} \text{ sec}[/tex] , the height of baseball will be 76 feet.
