If a projectile is fired from the origin with an initial velocity of 0 meters per

If a projectile is fired from the origin with an initial velocity of ν₀ meters per second at an angle α above the horizontal and air resistance is assumed to be negligible, then its position  after t seconds is given by the parametric equations

where t is the acceleration due to gravity (9.8 m/s²).

(a) If a gun is fired with α = 30° and ν₀ = 500 m/s, when will the bullet hit the ground? How far from the gun will it hit the ground? What is the maximum height reached by the bullet?

(b) Use a graph to check your answers to part (a). Then graph the path of the projectile for several other values of the angle α to see where it hits the ground. Summarize your findings.

(c) Show that the path is parabolic by eliminating the parameter.

Transcribed Image Text:

x = (vo cos a)t y = (vo sin a)t – igt? %3D