A ball is thrown from an initial height of 7 feet with an initial upward velocity of 24 fts. The ball's height h (in feet) after seconds is given by the following.
h=7+24t-16t^2
Find all values of t for which the ball's height is 11 feet.
Round your answer(s) to the nearest hundredth.

The ball's height is 11 feet at t = 0.19s and t = 1.31s

Step-by-step explanation:

The ball's height h (in feet) after seconds is given by the following function:

Find all values of t for which the ball's height is 11 feet.

This is t when .

We will need to solve a quadratic equation for this.

Solving a quadratic equation

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

In this problem:

Simplifying by 4

So

The ball's height is 11 feet at t = 0.19s and t = 1.31s

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