Question

Create a quadratic function for the given problem and then solve by using a graphing calculator. If necessary, round your answer to the nearest hundredth.

An egg falls from a nest in a tree 31 feet off the ground and lands on a potted plant that is 24 feet below the nest. The function h(t) = -16t^2 + 31 gives the height in feet of the egg as it drops, where t represents time. When will the egg land on the plant?

The egg will hit the plant after about _____ seconds.

a) 0.57
b) 0.82
c) 1.13
d) 2.27

Answer 1

The egg will land on the plant after approximately 0.82 seconds.

Step-by-step explanation:

To find when the egg will land on the plant, we need to solve the quadratic equation -16t^2 + 31 = 0. Using the quadratic formula, t = (-b ± √(b^2 - 4ac))/(2a), we can substitute a = -16, b = 0, and c = 31 into the formula. The discriminant, b^2 - 4ac, is positive, so we will have two solutions.

Calculating the quadratic formula, we get t = (-0 ± √(0^2 - 4*(-16)*31))/(2*(-16)). Simplifying further, t = (√(1984))/(32) or t = -√(1984))/(32). Since time cannot be negative, we take the positive solution: t ≈ 0.82 seconds.