Quadratic Word Problem

Question

Layla is on top of a building. Kate look up to see her at an angle of elevation of 35 degrees, she is 200 ft away. Layla pick up a rock and throw it down at 60 ft/sec. If Kate is 6 ft tall, how long until the rock hit the ground? Round to the nearest hundredth.

Answer 1

You don't specify what your class has been using for the acceleration of gravity. I will assume it to be -32.174 ft/s²

Looking at the details, we can draw a picture:

tan(35°) = h₁/200 so h₁ = 200tan(35°) = 140.0415 ft

h_total = h₁ + 6 = 146.0415 ft

The equation for the time an object that is thrown down and under gravitational force takes to hit the ground is:

x = v_it + 1/2at² where x is the distance or height, in this case -146.0415 ft, v_i is the initial velocity which in this case is -60 ft/s, a is the acceleration of gravity which is -32.174 ft/s² so:

-146.0415 = -60t + 1/2(-32.174)t² or writing in in standard form and combining:

-16.087t² - 60t + 146.0415 = 0

We can solve using the quadratic formula t = [-b ± √(b² - 4ac)]/(2a) = (60 ± √12997.478)/-32.174 = 1.68 s (or -5.41 s which we can throw out)