Asked by Anonymous
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.
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.
Answers
Answered by
oobleck
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
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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