From the roof of a building 125 feet above the ground, you toss a coin upward with an initial velocity of 11 feet per second. The height h (in feet)of the coin at time t (in seconds)after it is tossed is modeled by $h = - 16 t ^ { 2 } + 11 t + 125$ . Find the time when the coin hits the ground. Round your answer to two decimal places
A)2.47 seconds
B)50.56 seconds
C)3.16 seconds
D)39.56 seconds
E)6.51 seconds

Question

Quizplus · Accepted Answer

To find the time when the coin hits the ground, we need to find when the height of the coin is equal to 0. So we can set h equal to 0 and solve for t.
$$0 = - 16 t ^ { 2 } + 11 t + 125$$
Using the quadratic formula,
$$t = \frac{ - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$$
where $a = -16$, $b = 11$, and $c = 125$.
$$t = \frac{ -11 \pm \sqrt { 11 ^ { 2 } - 4 ( -16 ) ( 125 ) } } { 2 ( -16 ) } \approx \boxed{3.16}$$
We can exclude choices A, B, D, and E since they differ significantly from our answer.

From the Roof of a Building 125 Feet Above the Ground