Question

Leon threw a rock off a cliff. the path of the rock is modeled by the equation h(t) = -16t2 10t 8, where h(t) represents the height of the rock from the ground. he wanted to find the time it would take for the rock to hit the ground below. when solving the equation h(t) = 0, leon found two times, -0.46 seconds and 1.09 seconds. are both times reasonable solutions to leon's question?

a. yes, both times are reasonable solutions since they both solve the modeling equation.
b. no, -0.46 seconds is the only reasonable solution since it is the first time the rock hits the ground.
c. no, 1.09 seconds is the only reasonable solution since the rock was thrown at t = 0.
d. no, neither time is a reasonable solution since it would take longer for the rock to hit the ground.

Answer 1

The only reasonable solution is 1.09 seconds since the rock was thrown at t = 0.

Step-by-step explanation:

The equation h(t) = -16t^2 + 10t + 8 models the height of a rock thrown off a cliff. To find the time it takes for the rock to hit the ground, we need to solve the equation h(t) = 0. Leon found two solutions, -0.46 seconds and 1.09 seconds. But only the positive solution, 1.09 seconds, is a reasonable answer since time cannot be negative in this context. Therefore, the correct answer is option c. No, 1.09 seconds is the only reasonable solution since the rock was thrown at t = 0.