The model for

Question

The model for the height of a projectile is h=-16t^2+by+s, where h is the height in feet, t is the time in seconds, v is the initial velocity in feet per second, and s is the initial height in meters. A football is punted from a height of 2.5 feet above ground with a initial velocity of 45 feet per second. Will the ball ever reach a height of 60 feet?

Answer 1

The "y" in the given equation should be a "t". Also, "s" must be the initial height in feet, not meters.

 

b = 45

s = 2.5

 

h = -16t² + 45t + 2.5

 

Set h = 45 and solve for t.

 

45 = -16t² + 45t + 2.5

 

-16t² + 45t - 42.5 = 0

 

You have here a quadratic equation in t.  To reach 45 feet, there must be a positive real solution to this equation.  Evaluate the discriminant and then decide what kind of solutions you will get out of this, and you can answer the question. If there is no real positive solution for t, you do not reach 45 feet. If there is a positive real solution for t, you do reach 45 feet.