Solve Problems Using Systems of Nonlinear Equations
-A Person at the Top

Solve Problems Using Systems of Nonlinear Equations
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation $h = - 16 t ^ { 2 } + 600$ where $h$ is measured in feet and $t$ is the number of seconds since the yellow ball was dropped. A second person, in the same building but on a lower floor that is 264 feet from the ground, drops a white ball 3 seconds after the yellow ball was dropped. The height of the white ball is given by the equation $h = - 16 ( t - 3 ) ^ { 2 } + 264$ where $h$ is measured in feet and $t$ is the number of seconds since the yellow ball was dropped. Find the time that the balls are the same distance above the ground and find this distance.

A) 5 seconds; 200 feet
B) 4 seconds; 344 feet
C) $4.5$ seconds; 276 feet
D) $5.5$ seconds; 116 feet