Field Goal Projectile Motion Problem: Calculating Angle and Speed for NFL Kicker

[Toranc3]

Homework Statement

Kicking a field goal. In U.S. football, after a touchdown the team has the opportunity to earn one more point by kicking the ball over the bar between the goal posts. the bar 10.0 ft above the gound, and the ball is kicked from ground level, 36ft horizontally from the bar. Football regulations are stated in english units, but convert to SI units for this problem. (a) there is a minimum angle above the ground such that if the ball is launched below this angle, it can never clear the bar, no matter how fast it is kicked what is this angle? (B) If the ball is kicked at 45deg above the horizontal, what must its initial speed be if it to just clear the bar? EXpress your answer in m/s and km/h

Homework Equations

y=yo+voy*t+1/2*a*t^(2)
x-xo=vox*t

The Attempt at a Solution

10ft= 3.048m
36ft= 10.9728m

x-xo+vox*t

10.9728m=vocos(θ)*t

y=yo+voy*t+1/2*a*t^(2)

3.048m=vosin(θ)*t -1/2*g*t^(2)

I have 3 unknowns with two equations. I am stuck on this one though. Could somebody give me a hint? Thanks!

 

[Andrew Mason]

Homework Statement

Kicking a field goal. In U.S. football, after a touchdown the team has the opportunity to earn one more point by kicking the ball over the bar between the goal posts. the bar 10.0 ft above the gound, and the ball is kicked from ground level, 36ft horizontally from the bar. Football regulations are stated in english units, but convert to SI units for this problem. (a) there is a minimum angle above the ground such that if the ball is launched below this angle, it can never clear the bar, no matter how fast it is kicked what is this angle? (B) If the ball is kicked at 45deg above the horizontal, what must its initial speed be if it to just clear the bar? EXpress your answer in m/s and km/h

Homework Equations

y=yo+voy*t+1/2*a*t^(2)
x-xo=vox*t

The Attempt at a Solution

10ft= 3.048m
36ft= 10.9728m

x-xo+vox*t

10.9728m=vocos(θ)*t

y=yo+voy*t+1/2*a*t^(2)

3.048m=vosin(θ)*t -1/2*g*t^(2)

I have 3 unknowns with two equations. I am stuck on this one though. Could somebody give me a hint? Thanks!

Use:

(1)$x = sin(45)v_{0}t$

(2)$y = x - \frac{1}{2}gt^2$

Solve for t in (2) using the values for the bar height (y) and distance (x). Then find v0 with (1).AM

 

[SteamKing]

The line of scrimmage is 36 feet from the bar, but the ball is snapped to a holder positioned behind the line of scrimmage, where the kick is made. This extra distance is usually about 7 yards behind the line of scrimmage.