Question

A tennis ball is hit into the air and can be modeled by h=16t*2++40t+3, where h is the height t is the time it takes the ball to travel.
1) At what time t does the ball reach its maximum height above the court? How high did the ball go?
2) How long did it take the ball to hit the ground?

h=16t*2+40t+3 t=-(40)/2(16)=-40/32

Answer 1

please use t^2 to show exponents.
the * symbol is traditionally used for a multiplication sign

h = -16t^2 + 40t + 3 , note the - sign!
dh/dt = -32t + 40
= 0 for a max of h
32t = 40
t = 40/32 = 1.25 seconds

when t = 1.25
h = -16(1.25)^2 + 40(1.25) + 3= 28

when it hits the ground, h = 0
0 = -16t^2 + 40t + 3
16t^2 - 40t - 3 = 0
by the formula
t = 2.57 or a negative