Question

A leaf fell from a tree. The path of the leaf can be modeled by the equation h(t) = -16t^2 + vt + h0, where h is the height of the leaf in feet, t is time in seconds. Determine how long it takes for the leaf to fall to the ground.

a) t = 0
b) t = 1
c) t = 2
d) t = 3

Answer 1

Without specific values for the initial velocity and height, we cannot calculate the exact time it takes for the leaf to fall to the ground. We solve the quadratic equation for h(t) = 0 using the quadratic formula, considering only the positive value of t.

Step-by-step explanation:

To determine how long it takes for the leaf to fall to the ground, we need to solve the equation h(t) = -16t^2 + vt + h0 when h(t) is equal to zero, indicating that the leaf has reached the ground. In this equation, v is the initial velocity of the leaf, and h0 is the initial height from which it fell. Since the question does not provide specific values for v and h0, we cannot compute the exact time without additional information. However, we can say that the solution to the equation is the time t when h(t) equals zero. If hypothetical values for v and h0 were known, one would typically use the quadratic formula to find the positive value of t that satisfies the equation. If we were to look at options a), b), c), and d), without specific numbers these simply represent possible times but are not solutions by themselves. To actually find the time it would take, we must know the initial conditions of the leaf's fall or solve the equation if given those values.