Answer :
a) The T-shirt will be at its maximum height when the velocity is at zero, because its velocity will be at zero when it reaches the top of its arc.
You have the position function, y= -16t^2 + 72t + 5, so the velocity function is its derivative, v= -32t + 72.
Set that equal to zero, 0= -32t + 72, and solve for t.
0= -32t + 72
32t = 72
t = 9/4 or 2.25 seconds.
b) Plug what you found in part a) back into your position equation.
-16(2.25)^2 + 72(2.25) + 5 = -81 + 162 + 5 = 86 feet
c) The t-shirt's lowest point is 5 feet above the ground (that's the '+ 5' in the position equation) and its highest point is 86 feet, which you found in part b). So the range is [5,86]
You have the position function, y= -16t^2 + 72t + 5, so the velocity function is its derivative, v= -32t + 72.
Set that equal to zero, 0= -32t + 72, and solve for t.
0= -32t + 72
32t = 72
t = 9/4 or 2.25 seconds.
b) Plug what you found in part a) back into your position equation.
-16(2.25)^2 + 72(2.25) + 5 = -81 + 162 + 5 = 86 feet
c) The t-shirt's lowest point is 5 feet above the ground (that's the '+ 5' in the position equation) and its highest point is 86 feet, which you found in part b). So the range is [5,86]
The maximum height of the T-shirt is 86 feet at 2.25 seconds. The range of the function is [5, 85]
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation y = -16t² + 72t + 5
The maximum height is at y' = 0, hence:
y' = -32t + 72
-32t + 72 = 0
t = 2.25 seconds
Maximum height = -16(2.25)² + 72(2.25) + 5 = 86 feet
The maximum height of the T-shirt is 86 feet at 2.25 seconds. The range of the function is [5, 85]
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