A projectile that was launched straight up from the ground with an initial velocity of 48 ft/s returned to the ground after 3 s. The height of the projectile t seconds after launch is modeled by the function f (t) = - 16t2+48t. What is the maximum height of the projectile, in feet?

Question

Mathematics

Damian Erickson

16 April, 06:07

A projectile that was launched straight up from the ground with an initial velocity of 48 ft/s returned to the ground after 3 s. The height of the projectile t seconds after launch is modeled by the function f (t) = - 16t2+48t. What is the maximum height of the projectile, in feet?

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Damari Jones · Answer 1

The time to reach maximum height is given by the formula t=-b/2a, where b is the linear term's coefficient and a is the quadratic term's coefficient. Plugging in the values, we find t=-48/-32=1.5 seconds. We can plug this back into the quadratic equation to get h=f (1.5) = 36 feet.