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.
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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,
so it's the smaller answer.
check answer
y = –16t2 + 80t
y = –(16 • 0.25) + (80 • 0.5)
y = –4 + 40
y = 36
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