A quarterback can throw 60yd @ 45 degree angle. How fast can he throw?

In summary, the conversation discusses how to calculate the speed of a quarterback's throw based on the distance and angle it travels. The solution involves setting up equations for the x and y directions and accounting for the acceleration due to gravity. The net displacement in the y-direction is 0, indicating that the ball is caught at the same height it was thrown from.
  • #1
xcgirl
20
0

Homework Statement



A quarterback can throw 60yd @ 45 degree angle. How fast can he throw?

Homework Equations



60 yds = 54.86 meters

The Attempt at a Solution



x-direction
d = vt
4.86 = vcos(45)(t)

y-direction
d = vt + 1/2at^2
d = vsin(45)t + 1/2(9.8)t^2

I want to solve for t in both equations, set them equal, and use that to solve for v but I don't know what to use for d in the y-direction equation. would it be zero because it ends up on the ground?
 
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  • #2
When the throw has been measured as having gone 60 yards, what does that mean? Is the ball still flying through the air?
 
  • #3
I think that it means that the ball is caught at the same height that it is thrown from, so its a net displacement in the y-direction is 0.
 
  • #4
xcgirl said:
I think that it means that the ball is caught at the same height that it is thrown from, so its a net displacement in the y-direction is 0.

Okay, so if you put that net y-displacement into your equation of motion for the y-direction, you should be able to solve for t in terms of the other variables in that equation.

Oh, and make sure that you account for the fact that the acceleration due to gravity is in the downward direction...
 
  • #5
thanks, i got it now!
 

1. What is the formula for calculating the speed of a quarterback's throw?

The formula for calculating the speed of a quarterback's throw is v = √(d * g)/sin(2θ), where v is the velocity, d is the distance thrown, g is the acceleration due to gravity, and θ is the throwing angle.

2. How far can a quarterback throw at a 45 degree angle?

Assuming all other variables (such as the quarterback's strength and throwing technique) remain constant, a quarterback can throw approximately 60 yards at a 45 degree angle.

3. Can a quarterback throw faster at a different angle?

Yes, a quarterback can potentially throw faster at a different angle. The optimal throwing angle for the farthest and fastest throw is estimated to be between 35-40 degrees.

4. How does air resistance affect the speed of a quarterback's throw?

Air resistance does have an impact on the speed of a quarterback's throw. The higher the air resistance, the slower the ball will travel. However, the impact of air resistance on the speed is minimal in short distances (less than 100 yards).

5. What is the average speed of a quarterback's throw?

The average speed of a quarterback's throw is around 50-60 miles per hour. However, this can vary greatly depending on the individual's strength and technique.

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