Question

A diver jumps off a diving board with an initial velocity of 4 m/s from a height of 5 m. The

equation h(t) = -4.9t^2+ 4t + 5 models the diver height in meters after t seconds. About how many seconds does it take for the diver to land in the water?

Answer 1

To find the time it takes for the diver to land in the water, we can set the equation h(t) = -4.9t^2 + 4t + 5 equal to zero and solve for t. The solutions are approximately 0.33s and 1.23s, but since time cannot be negative, the diver takes approximately 1.23 seconds to land in the water.

Step-by-step explanation:

To find the time it takes for the diver to land in the water, we need to determine when the height h(t) is equal to zero. We can set the equation h(t) = -4.9t^2 + 4t + 5 equal to zero and solve for t.

-4.9t^2 + 4t + 5 = 0

Using the quadratic formula, we can find the values of t:

t = (-4 + sqrt((4^2) - (4 * -4.9 * 5)))/(2(-4.9)) and t = (-4 - sqrt((4^2) - (4 * -4.9 * 5)))/(2(-4.9))

Solving for t results in two solutions: t = 0.33s and t = 1.23s. Since time cannot be negative, the diver takes approximately 1.23 seconds to land in the water.