+586 The equation y = -16t^2 + 60t describes the height (in feet) of a projectile launched from the ground at 60 feet per second upward. In how many seconds will the projectile first reach 56 feet in height? Express your answer as a decimal rounded to the nearest hundredth.
Solve for t:
56 = 60 t - 16 t^2
56 = 60 t - 16 t^2 is equivalent to 60 t - 16 t^2 = 56:
60 t - 16 t^2 = 56
Divide both sides by -16:
t^2 - (15 t)/4 = -7/2
Add 225/64 to both sides:
t^2 - (15 t)/4 + 225/64 = 1/64
Write the left hand side as a square:
(t - 15/8)^2 = 1/64
Take the square root of both sides:
t - 15/8 = 1/8 or t - 15/8 = -1/8
Add 15/8 to both sides:
t = 2 or t - 15/8 = -1/8
Add 15/8 to both sides:
t = 7/4 = 1.75 seconds. But after 1.75 seconds it continues to go up for about 1/4 foot. And coming down to 56 feet again at exactly t= 2 seconds.
Note: somebody should check this.
