Answer:
The maximum height is 46.64 feet.
Step-by-step explanation:
If we take the derivative of h whit respect to t and equal this to zero we would find the value of t which corresponds to the maximum h.
So, we have the function h(t):
[tex]h(t)=-16t^{2} + 45t + 15[/tex]
Taking the derivative, we have:
[tex]\frac{dh(t)}{dt}=-32t + 45=0[/tex]
Now, we solve it for t:
[tex]t=\frac{45}{32}=1.4\: s[/tex]
Finally, we put this value of t into the original equation.
[tex]h(t)=-16(1.4)^{2} + 45(1.4) + 15[/tex]
[tex]h_{max}=46.64\: ft[/tex]
Therefore, the maximum height is 46.64 feet. All the given options are wrong, the one that comes closest is option A.
I hope it helps you!
