Write a quadratic function to model the vertical motion for each situation, given h(t) equals negative 16t squared plus v0t+h0. Find the maximum height. Initial vertical velocity: 96 ft/s; initial height: 50 ft

hmax = 194 ft

The maximum height is 194 ft

Step-by-step explanation:

According to the given equation for the model of the vertical motion. The height at any point in time can be written as;

h(t) = -16t^2 + v0t + h0 1

Where;

h(t) = height at time t

t = time

v0 = initial velocity = 96 ft/s

h0 = initial height = 50 ft

To determine the maximum height we need to differentiate the equation 1 to find the time at which it reaches maximum height;

At the highest point/height h' = dh/dt = 0

h'(t) = -32t +v0 = 0

-32t + v0 = 0

t = v0/32

t = 96/32

t = 3 s

At t=3 it is at maximum height.

The maximum height can be derived from equation 1;

Substituting the values of t,v0,h0 into equation 1;

h(t) = -16t^2 + v0t + h0 1

hmax = -16(3)^2 + 96(3) + 50 = 194 ft

hmax = 194 ft

The maximum height is 194 ft

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step-by-step explanation:

at least i think its