Field goal problem

A Field Goal

The Story of the Giant’s kicker

Josh Brown’s

Longest Attempt

•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:

• Assuming the crossbar is 3 m high, does his kick make it over the crossbar?

• 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

• 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=?

• 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

• 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

• 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

• 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!”

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?!?!?!!!!

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?

• 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!!!