Answer:
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
