field goal problem
DESCRIPTION
A quick upload of the Field Goal problem from class.TRANSCRIPT
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A Field Goal
The Story of the Giant’s kicker
Josh Brown’s
Longest Attempt
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•Josh Brown, the Giant’s Field Goal kicker is attempting his personal best field goal from the 52 yard line (~48 m).
• If the kick leaves the ground at 25 m/s at an angle of 30o, Determine the following:
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• Assuming the crossbar is 3 m high, does his kick make it over the crossbar?
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• Step One: Determine the X and Y components of the original Launch Velocity
• Vix=(25 m/s) x cos(30o) = 21.65 m/s
• Viy=(25 m/s) x sin(30o) = 12.5 m/s
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• Organize your Givens into an X/Y Chart:
X | Y-----------------------------------------------Vix=21.65 m/s | Viy=12.5 m/sVfx=Vix=Vavex | Vfy=Vapexy = 0 m/sax=0 m/s2 | ay=-9.81 m/s2
dx=48 m | dy=?----------------------------------------------- t=?
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• Step 3: Determine the time to travel to the goal post:
dx=Vix x t
48 m = 21.65 m/s x t
t = 2.217 s
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• Step 4: Determine the time to the apex:
Vfy = Viy + ay x t
0 m/s = 12.5 m/s + (-9.81 m/s2) x t
t = 1.274 s
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• SO…… that means that after reaching the apex of the flight at 1.2742 s, the football fell from the apex for an additional 0.943 s(2.2172 s - 1.274 s). The questions is….how far did you fall from the apex.
If you set Viy to 0 m/s at the apex, then the displacement equation tells how far you fell:
dy = (viy x t) + 1/2 x ay x t2
dy = 0 + (0.5 x -9.81 m/s2 x (0.943 s)2
dy = -4.36 m
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• The Max height (apex) can be determined using the displacement equation:
dmax = (12.5 m/s x 1.274 s) + (0.5 x -9.81 m/s2 x (1.274 s)2)
dmax = 7.976 m
So, at the crossbar, the football was 3.616 m from the ground….easily clearing the 3 m crossbar
“He Shoots! He Scores!”
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Did I really need to do ALL that????
If I know that the ball must stay in the air for 2.217s to reach the crossbar horizontally, what would the vertical displacement be if I solved using that time?
dy = (Viy x t) + ((1/2 x ay x (t2))
dy = (12.5 m/s x 2.217 s) + ((0.5 x -9.81 m/s2 x (2.217 s)2)
dy = 3.61 m !!! The SAME height above the ground we calculated previously!!
AIN’T PHYSICS GREAT?!?!?!!!!
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BUT WHAT ABOUT THE “D”?
• If Terrell Brown (6’11” Defensive lineman) is able to reach his hands up 2.9 m at a distance of 7 m from the kick (line of scrimmage), Does he block it?
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• The kick will travel the 7 m to the line of scrimmage in 0.32 s. The kick will rise from the
ground a distance of 3.53 m, clearing the outstretched arms of Terrell Brown by 0.63 m
• (~ 2 ft).
So Brown beats Brown!
HE SHOOTS! HE SCORES!!!