Question

Susan throws a softball upward into the air at a speed of 32 feet per second from a 88 dash foot88-foot platform. the distance upward that the ball travels is given by the function d left parenthesis t right parenthesis equals negative 16 t squared plus 32 t plus 88d(t)=−16t2+32t+88. what is the maximum height of the​ softball? how many seconds does it take to reach the ground after first being thrown​ upward? ​ (round your answer to the nearest​ tenth.)

Answer 1

D(t)=-16t²+32t+88
a] Maximum height
At maximum height d'(t)=0
from d(t);
d'(t)=-32t+32=0
thus
t=1
hence the maximum height will be:
d(t)=-16t²+32t+88
d(1)=-16(1)^2+32(1)+88
d(1)=104 ft

2]  how many seconds does it take to reach the ground after first being thrown​ upward? ​
Here we solve for t intercept
when d(t)=0
thus
0=-16t²+32t+88
solving for t, we get:
t=1-√13/2
or
t=1+√13/2

t=-1.55 or t=3.55 sec
Thus the answer is t=3.55 sec