Question

3. A soccer player heads a ball from a height of 6 feet with an initial vertical velocity of 20 feet per second. The height h in feet of the ball is given by h= –16t + 20t +6,

where t is the time elapsed in seconds. How long will it take the ball to hit the
ground if no other players touch it? State the method you used to solve this
quadratic equation and why you chose that method.

Answer 1

Part A

1.5 seconds

Part B

By substitution and factorization because h = 0 at ground level

Explanation:

Part A

The height from which the soccer player heads the ball, h = 6 feet

The initial velocity of the ball, v = 20 ft./s

The height of the ball in feet, h = -16·t² + 20·t + 6

From the given equation of the ball, we have;

At the initial height, t = 0, from the given equation, h = 6

At the ground level, the height, h = 0, therefore, we get;

0 = -16·t² + 20·t + 6

Factorizing using a graphing calculator gives;

0 = 2 × (-8·t² + 10·t + 3) = -2 × (8·t² - 10·t - 3) = -2 × (2·t -3)·(4·t + 1)

∴ (2·t -3)·(4·t + 1) = 0

t = 1.5 or t = -1/4 = -0.25

Therefore;

The time it takes the ball to hit the ground, t = 1.5 seconds.

Part B

The method used in solving the given quadratic equation is by plugging in the value of 'h' as h = 0 in the given equation and factorizing the result because at ground level, the height, h = 0.