Nonlinear Equations

Question

1. A bird starts flying up from the grass in a park and climbs at a steady rate of 0.5 meters per second. is height h in meters after t seconds is given by h=0.5t. The equation h=-4.9t^2+40t+3 models the height h, in meters, of a baseball t seconds after it is hit. find the time it takes for the ball in the bird to reach the same height.

 

2.  The deer population in a park can be modeled by the equation P(y)=4y^2-10y+60, where y is the number of years after 2010. The deer population in another park can be modeled by P(y)=10y+80, where y is the number of years after 2010. In which year will the two parks have approximently the same number of deer?

Answer 1

1)

 

Since the ball and bird are going to meet at the same height, simply set the two equation equal to each other.

 

0.5t = -4.9t² + 40t + 3

 

 

Subtract 0.5t to both sides of the equation.

 

0 = -4.9t² + 39.5t + 5

 

 

Solve this quadratic equation for x.  Choose the positive value of t.

 

 

2)

 

Set the P(y) equations equal to each other.  You will do the same procedure from question 1.  You should end up with a quadratic equation.  The solve for y from that quadratic equation.  Choose the positive of y.  The value of y should be an integer.  If not, then round to the nearest integer.  Then take that value of y and add it to 2010 to get your year.