The Position After T Seconds of a Projectile Red with Initial

question 57

Essay

The position after t seconds of a projectile red with initial velocity v0 (measured in ft/s) at an angle above the horizontal from an initial height of h0 (measured in ft) is given by the parametric equations $x = \left( v _ { 0 } \cos \alpha \right) t$ $y = \left( v _ { 0 } \sin \alpha \right) t - 16 t ^ { 2 } + h _ { 0 }$ .
(a) Eliminate the parameter t to show that the trajectory of the projectile is a parabola.
(b) If the projectile is red with an initial velocity of 300 ft/s from a height of 5 ft, what should be the angle of elevation in order to hit a target at the same height as the initial height, 900 ft downrange?
(c) If the projectile is red with an angle of elevation of 40 ^$\circ$ and it strikes a target at the same height as the initial height, 600 ft downrange, what was the initial velocity of the projectile?

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