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The equation  y=-16t^2 +80t describes the height (in feet) of a projectile launched from the ground at 80 feet per second. At what  t will the projectile reach 36 feet in height for the first time? Express your answer as a decimal rounded to the nearest tenth.

Aug 2, 2023

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The equation  y=-16t^2 +80t describes the height (in feet) of a projectile launched from the ground at 80 feet per second. At what  t will the projectile reach 36 feet in height for the first time? Express your answer as a decimal rounded to the nearest tenth.

y  =  –16t2 + 80t describes the height, so let's just set y to the desired height and see what happens.

36  =  –16t2 + 80t

Subtract 36 from both sides.                       0  =  –16t2 + 80t – 36

Multiply both sides by –1.                         16t2 – 80t + 36  =  0

Divide both sides by 4, to get

more manageable coefficients.                   4t2 – 20t + 9  =  0

Factor.                                                        (2t – 1)(2t – 9)  =  0

2t  =  1      ----->  t  =  0.5 sec

and  2t  =  9      ----->  t  =  4.5 sec

The problem asks for the time

to get to 36 feet on the way up,

y  =  –16t2 + 80t

y  =  –(16 • 0.25) + (80 • 0.5)

y  =  –4 + 40

y  =  36

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Aug 2, 2023