Question

A ball is thrown from an initial height of 4 feet with an initial upward velocity of 33 ft/s. The ball's height h (in feet) after t seconds is given by the following.

h= 4 + 33t - 16t^2

Find all values of t for which the ball's height is 20 feet.

Round your answer(s) to the nearest hundredth.

(If there is more than one answer, use the "or" button.).

Answer 1

At both 0.78 and 1.3 seconds, to the nearest hundredth, the ball will be at 20 feet.

Explanation:

We can use two approaches to finding the answer: Calculation and Graphing.

Calculation:

Set h to 20 feet and solve the equation using the quadratic formula.

h= 4 + 33t - 16t^2

20= 4 + 33t - 16t^2

- 16t^2 + 33t + 4 = 20

- 16t^2 + 33t + -16 = 0

Solve using the quadratic formula. I find solutions of 0.779 and 1.28 seconds.

Graphing:

See the attached graph.

The ball is at 20 feet at 0.783 seconds on the way up and 1.28 seconds on the way back down.

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Both approaches agree: 0.78 and 1.3 seconds, to the nearest hundredth, the ball will be at 20 feet.