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Mathematics

A quarterback is standing on the football field preparing to throw a pass. His receiver is
standing 20 yards down the field and 15 yards to the quarterback's left. The quarterback
throws the ball at a velocity of 60 mph towards the receiver at an upward angle of 30° (see
the following figure). Write the initial velocity vector of the ball V, in component form.

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  1. If you draw a diagram, you can see that the direction of the ball is at an angle θ left of directly downfield, where tanθ = 3/4
    So, if we set up an x-y-z coordinate system with origin at the quarterback, and
    downfield in the +x direction, then the components of v (in mi/hr) are
    vx = 60 cos30° cosθ = 60 * √3/2 * 2/5 √3
    vy = 60 cos30° sinθ = 60 * √3/2 * 3/5 = 18/5 √3
    vz = 60sin30° = 30

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