Projectile math question

Question

Eyjafjallajökull is a volcano in Iceland. IN a recent eruption a projectile is ejected with an initial velocity of 304 feet per second.

The height,H, in feet is given by the equation H= -16t2+304t

where t is the time in seconds

1. determine the time it takes the projectile to reach its heights point
2. the maximum height of the projectile
3. the time it takes the projectile to return to the ground

Answer 1

take the derivative and set equal to zero, solve for t=time to reach max height

H' = -32t + 304 = 0

t = 304/32 = 76/8 = 38/4 = 19/2 = 9.5 seconds to reach maximum height

Plug t=9.5 into the H equation to calculate max height

H(9.5) = -16(9.5)^2 + 304(9.5) = 9.5(-16(9.5)+304)= 1444 feet

H=0 = -16t^2 + 304t = t(-16t +304)

t = 304/16 = 76/4 = 19 seconds to hit the ground