The height of a projectile launched upward at a speed of 32 feet/second from a height of 48 feet is given by the function: h(t)=-16t^2+32t+48. How long will it take the projectile to hit the ground?

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Answer 1 · 2018-06-05T05:54:30

The time is #=3s#

The height is given by

#h(t)=-16t^2+32t+48#

When #t=0#

#h(0)=0+0+48 ft#

This is the initial cionditions.

The projectile will hit the ground when #h(t)=0#

Therefore,

#-16t^2+32t+48=0#

#<=>#, #16t^2-32t-48#

#<=>#, #16(t^2-2t-3)=0#

#<=>#, #(t+1)(t-3)=0#

#<=>#, #{(t=-1),(t=3):}#

Therefore,

the time is #=3s#

graph{-16x^2+32x+48 [-104.7, 132.45, -47.2, 71.5]}