## Harrison plays a game in which he uses a net to catch balls that are randomly launched from holes in the ground. The height of one ball afte

Question

Harrison plays a game in which he uses a net to catch balls that are randomly launched from holes in the ground. The height of one ball after t seconds is represented by the function f(t) = –16t2 + 20t. After how many seconds does the ball return to the ground? Round to the hundredths place as needed. seconds

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1 month 2021-10-18T12:43:15+00:00 2 Answers 0 views 0

Step-by-step explanation:

Given

f(t) = -16t² + 20t

Required

After what time (in seconds) does the ball return to the ground?

Function f(t) is a function of time and it represents the displacement of the ball.

For the ball to return to the ground, it means the displacement is 0.

So, we have f(t) = 0.

Substitute 0 for f(t) in the above, we have

0 = -16t² + 20t —- Factorize

0 = -4t(4t – 5) —- Reorder

-4t(4t – 5) = 0

This above expression can be splitted to;

-4t = 0 or 4t – 5 = 0

For -4t = 0,

divide through by -4

This will give t = 0

For 4t – 5 = 0,

Collect like terms

4t = 5 + 0

4t = 5

Divide through by 4

t = 5/4

t = 1.25

So, we have that

t = 0 or t = 1.25

But t can’t be 0 because the ball has already traveled some distance.

So, t = 1.25