At time t=0, in seconds, a pair of sunglasses is dropped from the Eiffel Tower in Paris. At time t, its height in feet above the ground is given by h(t)=−16t^2+1000.
When do the sunglasses hit the ground? Include units in your answer.
I got that the height is 1000ft and I have tried factoring it but I am not sure where to go now. I can't figure out how to set it up.
when it hits the ground, the height is zero. So, just solve
-16t^2 + 1000 = 0
16(62.5-t^2) = 0
t = √62.5 = 7.9
To find when the sunglasses hit the ground, we need to find the value of t when the height, h(t), is equal to zero. So we need to solve the equation −16t^2 + 1000 = 0.
Step 1: Set the equation equal to zero:
−16t^2 + 1000 = 0
Step 2: Divide both sides of the equation by −16 to isolate t^2:
t^2 - 62.5 = 0
Step 3: Add 62.5 to both sides of the equation to further isolate t^2:
t^2 = 62.5
Step 4: Take the square root of both sides of the equation to solve for t:
t = ± √(62.5)
Step 5: Simplify the square root of 62.5:
t ≈ ±7.905
Since time cannot be negative in this context, we can disregard the negative solution.
Therefore, the sunglasses hit the ground approximately 7.905 seconds after they were dropped.