The position of a projectile fired with an initial velocity v 0 feet per second and at an angle to the horizontal at the end of t seconds is given by the parametric equations See the illustration (a) Obtain the rectangular equation of the trajectory and identify the curve (b) Show that the projectile hits the ground when (c) How far has the projectile traveled (horizontally) when it strikes the ground In other words, find the range R (d) Find the time t when x y Then find the horizontal distance x and the vertical distance y traveled by the projectile in this time Then compute (x 2 y 2 ) This is the distance R, the range, that the projectile travels up a plane inclined at 45 to the horizontal (x y) See the following illustration (vo cos 0)t y (vo sin 0)t 1612 R

Question: The position of a projectile fired with an initial velocity v 0 feet per second and at an angle to the horizontal at the end

The position of a projectile fired with an initial velocity v₀ feet per second and at an angle to the horizontal at the end of t seconds is given by the parametric equations

See the illustration.

(a) Obtain the rectangular equation of the trajectory and identify the curve.

(b) Show that the projectile hits the ground when

(d) Find the time t when x = y. Then find the horizontal distance x and the vertical distance y traveled by the projectile in this time. Then compute √(x² + y²). This is the distance R, the range, that the projectile travels up a plane inclined at 45° to the horizontal (x = y). See the following illustration.

(vo cos 0)t y = (vo sin 0)t - 1612 R

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