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Julli [10]
3 years ago
15

A soccer ball is kicked into the air from a height of 3 feet with an initial velocity of 72 feet per second. How many seconds is

the ball 84 feet above the ground?
Mathematics
1 answer:
Veronika [31]3 years ago
3 0

Answer:

For 2.25 seconds the ball is 84 feet above the ground.

Step-by-step explanation:

Initial height when the ball is kicked = 3 feet

Initial velocity of the soccer ball = 72 feet per second

The height(h) of the vertical thrown object is modeled by the formula :

h(t) = -16t² + vt + s , where t is the time, v is initial velocity and s is initial height

Now, h(t) is given to be 84 feet and we need to find the time taken by the ball to reach 84 feet above the ground :

84 = -16t² + 72t + 3

⇒ 16t² - 72t + 81 = 0

Finding roots of this equation :

t = \frac{72\pm\sqrt{72^2-4\times 16\times 81}}{2\times 16}\\\\\implies t = \frac{72\pm 0}{32}\\\\\implies t = 2.25

Hence, for 2.25 seconds the ball is 84 feet above the ground.

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