Question

A basketball is shot from 7 feet high with an upward velocity 25ft/sec. Write a vertical motion model to see if the ball reaches a height of 16 feet. Find the discriminant. Does the ball reach a height of 16 feet?

Answer 1

$\huge{\mathbb{Question:-}}$

A basketball is shot from 7 feet high with an upward velocity 25ft/sec. Write a vertical motion model to see if the ball reaches a height of 16 feet. Find the discriminant. Does the ball reach a height of 16 feet?

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$\huge{\underline{\sf{\blue{Solution}}}}$

❥..The height h as a function of time t is

❥...h(t) = -16t2 + 20t + 6,

with t in seconds, h in ft.

To find when the ball reaches 10 ft, set h = 10 and solve for t.

❥.10 = -16t2 + 20t + 6

❥..-16t2 + 20t - 4 = 0

❥...Solve the quadratic equation for t and get t = 0.25 sec and 1 sec. Since both are positive, it takes the ball 0.25 sec to reach 10 ft on the way up, and 1 sec to reach 10 ft again on the way down. Since you want the ball to fall through the basket at 10 ft, use the time it takes coming back down to 10 ft, so your final answer is 1 sec.!¡!

$\huge {\boxed{\red{Thanks:-}}}$