Question

A ball is launched from a 682.276 meter tall platform. the equation for the ball's height h at time t seconds after launch is h(t) = -4.9t^2 + 682.276, where h is in meters. what is the maximum height the ball achieves before landing?

Answer 1

The maximum height the ball achieves before landing is 682.276 meters at t = 0.

What are maxima and minima?

Maxima and minima of a function are the extreme within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.

We have a function:

h(t) = -4.9t² + 682.276

Which represents the ball's height h at time t seconds.

To find the maximum height first find the first derivative of the function and equate it to zero

h'(t) = -9.8t = 0

t = 0

Find second derivative:

h''(t) = -9.8

At t = 0; h''(0) < 0 which means at t = 0 the function will be maximum.

Maximum height at t = 0:

h(0) = 682.276 meters

Thus, the maximum height the ball achieves before landing is 682.276 meters at t = 0.

Learn more about the maxima and minima here:

brainly.com/question/6422517

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