Solve a system of equations and interpret the solutions and if they are valid. explain

Question

The elevation of a rock dropped from the top of a building that is 300 meters tall is modeled by h=300-4.9t², where t is the time in seconds after the rock was dropped and h is its elevation in meters. At the same time, a bird in front of the building is rising into the air with an elevation described by h=2.7t+41. Solve the system of equations, and interpret the solution(s). is/are the solution(s) valid/ Why or why not?

Answer 1

I guess you intend to set the two equations equal to each other, solve for t, then explain what it means, right?

 

300 - 4.9t² = 2.7t + 41

 

0 = 4.9t² + 2.7t - 259

 

Use the quadratic formula:

 

t = (-2.7 ± √[2.7² - 4·1.9·(-259)])/(2·4.9)   (sorry for all the parentheses)

   = (-2.7 ± √1975.69)/9.8

 

Only the solution with the + makes sense here, and it is t ≈ 4.26 sec.

 

This is the time when the bird and rock have the same height. You could find the height by plugging this time into either equation for h and calculating the answer.