Question

You are jumping on a trampoline. For one jump, your height y (in feet) above the trampoline after t

seconds can be represented by y = -16t² + 24t.
How many seconds does it take to reach your highest point in the air?

Answer 1

To find the time it takes to reach the highest point, you need to identify the time at which the velocity is zero. In this case, the velocity function is the derivative of the height function.

The velocity function (v) is given by the derivative of the height function (y):

\[ v(t) = \frac{dy}{dt} \]

Let's find \( v(t) \) by taking the derivative of \( y(t) = -16t^2 + 24t \):

\[ v(t) = -32t + 24 \]

Now, set \( v(t) \) to zero and solve for \( t \):

\[ -32t + 24 = 0 \]

\[ -32t = -24 \]

\[ t = \frac{24}{32} = \frac{3}{4} \]

So, it takes \( \frac{3}{4} \) seconds to reach the highest point.