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A projectile is launched from the ground at a angle with altitude (in feet after seconds) given by . Its horizontal displacement in feet is given by .

  1. Find an expression for the velocity vector as a function of .

  2. Calculate the magnitude of the velocity vector at and at the moment when the projectile hits the ground. Make a conjecture about the speed with which projectiles return to earth.

    To determine when the projectile hits the ground, solve .
    The velocity vector when is:
    Sketch this vector and use the Pythagorean Theorem to determine its magnitude.