Expert: Scotto - 6/10/2010

Question
If i were to throw a football from a height of 5 feet off the ground at a velocity of 45 feet/second.. How far will the football travel?
The equation i have come up with is -16T^2-45T+5. Is this not correct?

Answer
The equation is -gt²/2 + vt + d, where g is gravity, v is initial velocity, and d is the
original height.  With the equation given, it looks like the initial velocity is straight
down since it is negative.

If it were at an angle with the ground of Θ thrown at 45f/s, thrown in an upwards direction,
the equation for height would be - 16t² + 45*sinΘ + 5.  The equation for how far the football
would travel would be 45*t*cosΘ.

The best angle to make it go te farthest is 45°.  The sin45° and cos45° are both √2/2.
The equations for height would then be -16t² + (22.5√2)t + 5 and the equation for distance
travelled would be (22.5√2)t.

To find out how far the football travells, use the quadratic equation to find the solution
to the parabola.  One solution will be positive and the other will be negative.  Put these
solutions into the horizontal equation to determine how far the football will go.

Note that the negative solution, when put into the horizontal equation, will tell you where
on the ground the football should have been thrown from to get to 5 feet off the ground at
45 feet per second.  The positive solution, when put into the horizontal equation, will say
how far the ball travelled.