Find initial velocity of projectile - 10 points best answer
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Find initial velocity of projectile - 10 points best answer

[From: ] [author: ] [Date: 12-07-02] [Hit: ]
V² = -g*x²/[2cos²Θ(y - xtanΘ - yi)] = 3163.V = 56.......
I need help with this question. I don't really understand where to start. The question is:
The quarterback of a football team releases a pass at a height of 7 feet above the
playing field, and the football is caught by a receiver 30 yards directly downfield at a height of
4 feet. The pass is released at an angle of 30 degrees with the horizontal. At what speed was
the football released?
Any help is appreciated

-
Let the point at which the ball was released = (0, 7)
Let the point at which the ball was caught = (90, 4)
Let g = the acceleration due to gravity = 32.2 ft/s²
Let V = the initial velocity.
Let Vy = the initial velocity in the y direction = (V)sin(30°) = .5V
Let Vx = the velocity in the x direction = (V)cos(30°) ={(√3)/2}V
The height, y(t), is:
y(t) = 7 + (0.5V)t - (1/2)(32.2)t²
The horizontal displacement is:
x(t) = {(√3)/2}V(t)
The time of flight is:
t = 60(√3)/V
Substitute this for t and make the height be 4:
4 = 7 + (0.5V)(60√3)/V - 16.1{(60√3)/V}²
-54.96 = -173880/V²
V = √{-173880/-54.96} = 56.24 ft/s

-
The time of flight is not needed

V² = -g*x²/[2cos²Θ(y - xtanΘ - yi)] = 3163.67 ft²/sec²

V = 56.25 m/s
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