A person jumps off a 20m high cliff into the water below. The height of the person above the ground at t time 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?
just solve for height=10:
10 = -5t^2+30
t = 2
Good, correct answer just not sure how you got it. I do but what are the steps
To find out how long it takes for the person to reach the halfway mark to the water, we need to determine the height at that halfway point.
The halfway point is half of the total height, which is 20 meters. So, the halfway point would be 20/2 = 10 meters above the ground.
The equation h = -5t^2 + 30 gives us the height of the person above the ground at time t. We can set this equation equal to 10 and solve for t.
-5t^2 + 30 = 10
First, let's isolate the variable on one side by subtracting 10 from both sides of the equation:
-5t^2 + 30 - 10 = 0
-5t^2 + 20 = 0
Next, let's divide both sides of the equation by -5 to simplify the equation:
(-5t^2 + 20) / -5 = 0 / -5
t^2 - 4 = 0
Now, we can solve for t by factoring the equation:
(t - 2)(t + 2) = 0
Setting each factor equal to zero and solving for t gives us:
t - 2 = 0 or t + 2 = 0
t = 2 or t = -2
Since time cannot be negative, we discard t = -2. Therefore, the person takes 2 seconds to reach the halfway mark to the water.
Therefore, it takes the person 2 seconds to reach the halfway mark to the water.