If h(t) represents the height of an object in feet above ground level at time t and h(t) is given by
h(t)=−16t^(2)+14t+10
find the height of the object at the time when the speed is zero.
The height of the object is h(t)= ___ feet.
Nevermind, I figured it out! I got 209/16 and it's correct.
To find the height of the object at the time when the speed is zero, we need to find the time(s) when the derivative of the height function, h'(t), is equal to zero.
First, let's find the derivative of the height function, h(t):
h(t) = -16t^2 + 14t + 10
h'(t) = -32t + 14
Next, set h'(t) equal to zero and solve for t:
-32t + 14 = 0
Adding 32t to both sides, we get:
32t = 14
Finally, divide both sides by 32:
t = 14/32
Simplifying, we have:
t = 7/16
So the time at which the speed is zero is t = 7/16.
To find the height of the object at this time, substitute t = 7/16 into the height function:
h(7/16) = -16(7/16)^2 + 14(7/16) + 10
Simplifying the expression, we get:
h(7/16) = - 49/16 + 49/8 + 10
h(7/16) = -49/16 + 98/16 + 160/16
h(7/16) = 209/16
Therefore, the height of the object at the time when the speed is zero is 209/16 feet.