The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height in feet. what is the maximum height the rocket reaches?

maximum height reached = 35 feet

and

Step-by-step explanation:

writing linear motion equations

where s is the total displacement, u the initial velocity, t the time travelled, and a is the acceleration.

given u = 48 ft/s, and a = acceleration due to gravity g = -9.8

1 m = 3.28 feet therefore g becomes -9.8×3.28

here negative sigh comes as acceleration due to gravity is in opposite direction of initial velocity.

therefore f(t) becomes

to find max height we should find differentiation of f(t) and equate it to 0

therefore we get 48 = 32.144t

t = 1.49 s

therefore max height f(1.49) = 71.67-36.67 = 35 feet

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Step-by-step explanation: