On Mars, if you hit a baseball, the height f the ball a time t would be modeled by the quadratic function h (t) + = - 1.85t^2+20t+1 is in seconds and h (t) is in meters a) when will the ball hit the ground?

b) how long will the ball be above 17m?

Question

Mathematics

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25 June, 15:10

On Mars, if you hit a baseball, the height f the ball a time t would be modeled by the quadratic function h (t) + = - 1.85t^2+20t+1 is in seconds and h (t) is in meters a) when will the ball hit the ground?

b) how long will the ball be above 17m?

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Answers (1)

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Amaris Holland · Answer 1

The ball will hit the ground when h (t) = 0 so

-1.85t^2+20t+1=0 using the quadratic formula for simplicity ...

t = (-20±√407.4) / - 3.7, since t>0

t = (-20-√407.4) / - 3.7 seconds

t≈10.86 seconds (to nearest hundredth of a second)

...

How long will the ball be greater than 17m, h (t) >17

-1.85t^2+20t+1>17

-1.85t^2+20t-16>0

t> (-20+√281.6) / - 3.7

t< (-20-√281.6) / - 3.7 approximately ...

t<9.94

t>0.87

0.87
0.88≤t≤9.93

9.93-0.88=9.05

So the ball will be greater than 17m for about 9.05 seconds.

On Mars, if you hit a baseball, the height f the ball a time t would be modeled by the quadratic function h (t) + = - 1.85t^2+20t+1 is in seconds and h (t) is in meters a) when will the ball hit the ground?b) how long will the ball be above 17m?

On Mars, if you hit a baseball, the height f the ball a time t would be modeled by the quadratic function h (t) + = - 1.85t^2+20t+1 is in seconds and h (t) is in meters a) when will the ball hit the ground?

b) how long will the ball be above 17m?