Question

A ball is thrown from an initial height of 5 feet with an initial upward velocity of 21 ft/s

h=5+21t-16t²
Find all values of t for which the ball's height is 11 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
initial
h
t = seconds

Answer 1

Answer: Rounding these values to the nearest hundredth, we have t ≈ 0.75 or t ≈ 0.50.

Explanation:

To find the values of t for which the ball's height is 11 feet, we can set up the equation h = 11 and solve for t.

The equation for the height of the ball at time t is given by:

h = 5 + 21t - 16t^2

Setting h = 11, we have:

11 = 5 + 21t - 16t^2

Now, rearrange the equation to form a quadratic equation:

16t^2 - 21t + 6 = 0

To solve this quadratic equation, we can factor it:

(4t - 3)(4t - 2) = 0

Setting each factor equal to zero and solving for t, we get:

4t - 3 = 0 or 4t - 2 = 0

Solving each equation separately:

For 4t - 3 = 0:

4t = 3

t = 3/4

For 4t - 2 = 0:

4t = 2

t = 1/2

Therefore, the values of t for which the ball's height is 11 feet are t = 3/4 or t = 1/2.

Rounding these values to the nearest hundredth, we have t ≈ 0.75 or t ≈ 0.50.