A person jumps off a 20m high cliff into water below. The height of the person above the ground at time t seconds is given by the equation h=-5t^2+30. How long does it take the person to reach the half way mark to the water?
10 = -5t^2 + 30
5t^2 = 20
t^2 = 4
t = 2
To find the time it takes for the person to reach the halfway mark to the water, we need to determine when the height (h) of the person is half of the total height of the cliff.
Given that the height above the ground (h) is given by the equation h = -5t^2 + 30, we can set h equal to half of the total height:
-5t^2 + 30 = 20/2
Simplify the equation:
-5t^2 + 30 = 10
Rearrange the equation:
-5t^2 = 10 - 30
-5t^2 = -20
Divide both sides of the equation by -5:
t^2 = 4
Take the square root of both sides to solve for t:
t = √4
t = 2
Therefore, the person takes 2 seconds to reach the halfway mark to the water.