11)
Spider Man is standing on a parade float tossing candy out to young boys and girls. The candy is thrown with a starting velocity of 10 feet per second from a height of 3 feet modeled by the
equation h = - 16t + 10t + 3
When trying to figure out when the candy will be 2 feet in the air, the constant in the quadratic formula will be
(1 point)
answer: 2
The candy will reach 2 feet in the air at
_________ seconds when rounding to the
nearest hundredth of second.
To find the time at which the candy will be 2 feet in the air, we set h = 2 and solve for t:
2 = -16t^2 + 10t + 3
0 = -16t^2 + 10t + 1
Using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / 2a
a = -16, b = 10, c = 1
t = (-10 ± √(10^2 - 4(-16)(1))) / 2(-16)
t = (-10 ± √(100 + 64)) / -32
t = (-10 ± √164) / -32
t = (-10 ± 12.81) / -32
t = (-10 + 12.81) / -32 or t = (-10 - 12.81) / -32
t = 2.81 / -32 or t = -22.81 / -32
t ≈ -0.09 or t ≈ 0.71
Rounding to the nearest hundredth of a second, the candy will be 2 feet in the air after approximately 0.71 seconds.