quadratic question

Question

If air resistance is ignored, a projectile such as a rifle bullet or a cannonball follows a parabolic path. Suppose a cannonball fired from the origin follows the graph
y = x − 0.0005x2,
where both x and y are measured in feet.

How far downrange will the cannonball hit the ground?

ft

Answer 1

y = -0.0005x²  + x

 

Y represents the height in feet and x represents the

horizontal distance travelled.  We want to find when

y = 0 other than at the origin.  Note: We know one root

will be at x=0 since we start at zero feet height at the origin.

 

-0.0005x² + x = 0

 

quadratic equation:  a=-0.0005, b = 1, c=0

 

x = [-1±√(1²-4(-0.0005)(0))]/(2(-0.0005))

 

x = [-1 ±√1]/(-0.0010)

x = 0

or

x = -2/(-0.001)

 

x = 2000 ft

 

The cannonball will travel 2000 ft horizontal

distance before striking the ground.