Question

An observation deck extends 311 feet out above a valley. The deck sits 261 feet above the valley floor. If an object is dropped from the observation deck, its height (h) in feet, after (t) seconds, is given by (h = -16t^2 + 261). How long will it take for the object to be 5 feet above the valley floor?

It will take (t) seconds for the object to be 5 feet above the valley floor.


a) 4
b) 6
c) 10
d) 2

Answer 1

To calculate how long it takes for an object to be 5 feet above the valley floor, the quadratic equation -16t^2 + 261 = 5 is solved to get two values of t. The longer time, 4 seconds, is the correct answer as it represents the time on the way down close to impact.

Step-by-step explanation:

The student's question involves finding the time t it takes for an object to reach a certain height above the valley floor when dropped from an observation deck. Given the equation for the object's height h at time t as h = -16t2 + 261, we need to determine the time when the object is 5 feet above the valley floor. To solve this, we set h = 5 and solve for t in the quadratic equation -16t2 + 261 = 5. Factoring and applying the quadratic formula yields two possible values of t. Since the object passes the 5-foot height twice (once while falling), we select the longer time, as it represents the time when the object is on the way down and about to hit the valley floor, which yields t = 4 seconds.