h(t)=-16t2+13t+1
find the height of the object at the time when the speed is zero.
To find the height of the object at the time when the speed is zero, we need to determine the value of t when the derivative of h(t), which represents the velocity, is equal to zero.
Step 1: Obtain the derivative of h(t)
The derivative of h(t) with respect to t represents the velocity function. So, let's find the derivative of h(t) = -16t^2 + 13t + 1.
h'(t) = -32t + 13
Step 2: Set the derivative equal to zero and solve for t
To find when the speed is zero, set h'(t) = 0 and solve for t.
-32t + 13 = 0
-32t = -13
t = (-13/-32)
t = 13/32
Step 3: Substitute the value of t into the original function to find the height
Now that we've found t = 13/32, substitute this value back into the original function h(t) = -16t^2 + 13t + 1 to find the corresponding height.
h(13/32) = -16(13/32)^2 + 13(13/32) + 1
Simplifying this expression will give you the height of the object at the time when the speed is zero.