Question

A waterfall has a height of 1500 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 20 feet per second. The​ height, h, of the pebble after t seconds is given by the equation h=-16t^2 + 20t + 1500. How long after the pebble is thrown will it hit the​ ground?

The pebble will hit the ground about [___] seconds after it is thrown.

A) 3.125 seconds
B) 5 seconds
C) 6.25 seconds
D) 7.5 seconds

Answer 1

The pebble will hit the ground about 3.125 seconds after it is thrown.

Step-by-step explanation:

To find how long it will take for the pebble to hit the ground, we need to set the equation h=-16t^2 + 20t + 1500 equal to 0 and solve for t. This is because when the pebble hits the ground, its height will be 0. We can then use the quadratic formula to solve for t. The equation becomes:

-16t^2 + 20t + 1500 = 0

Using the quadratic formula, t = (-b ± sqrt(b^2 - 4ac)) / (2a) where a = -16, b = 20, and c = 1500. Plugging in these values, we get:

t = (-20 ± sqrt(20^2 - 4(-16)(1500))) / (2(-16))

t ≈ 3.125 or t ≈ 7.5

Since we are only looking for the time it takes for the pebble to hit the ground, we take the positive value, t ≈ 3.125 seconds. Therefore, the correct answer is A) 3.125 seconds.