A rock is thrown with a height equation of h = -16t2 + 20t + 5 (where h is the height of the rock in feet at any given time of t in seconds). Will it reach a height of 30 feet? Explain your answer.

Question

A rock is thrown with a height equation of h = -16t² + 20t + 5 (where h is the height of the rock in feet at any given time of t in seconds). Will it reach a height of 30 feet? Explain your answer.

Answer 1

Here's how you would solve this equation using algebra:

h = -16t² + 20t + 5, where h = height, t = time, the initial velocity = 20 ft/s and the 5 represents the initial height the rock was thrown from, acceleration of gravity = -16*2 = -32 ft/s²

Find when the height is 30 feet: 30 = -16t² + 20t + 5

Solve the equation by setting it equal to zero (subtracting 30 from both sides): -16t² + 20t - 25 = 0

Use the quadratic formula to find times when the rock is 30 feet in the air:

t = (-20± sqrt (20² - 4(-16)(-25))/(2*-16); t = (-20± sqrt(-1200))/(-32)

The square root of -1200 is imaginary. This means the rock will never get 30 feet high.

Using Calculus or a graphing calculator you can find that the maximum height of 11.25 feet occurs around t = .625 seconds

Answer: The rock will never get 30 feet high.