Question

a ball is thrown upward with an initial height of 3 feet with an initial upward velocity 37 ft/s the balls heigh in feet after t second is given by h=3=+37t-16t^2

Answer 1

`t = 1.45` or
`t = 0.86`

Explanation:

Given

`h=3+37t-16t^2`

Required

Find all values of t when height is 23 feet

To solve this, we simply substitute 23 for h

`23=3+37t-16t^2`

Collect like terms

`16t^2 - 37t - 3 + 23=0`

`16t^2 - 37t +20=0`

Solve t using quadratic formula;

`t = (-b\±√(b^2 - 4ac))/(2a)`

Where a = 16, b =-37 and c = 20

`t = (-(-37)\±√((-37)^2 - 4*16*20))/(2*16)`

`t = (37\±√((-37)^2 - 4*16*20))/(2*16)`

`t = (37\±√(1369 - 1280))/(32)`

`t = (37\±√(89))/(32)`

`t = (37\±9.43)/(32)`

`t = (37+9.43)/(32)` or
`t = (37-9.43)/(32)`

`t = (46.43)/(32)` or
`t = (27.57)/(32)`

`t = (46.43)/(32)` or
`t = (27.57)/(32)`

`t = 1.45` or
`t = 0.86`