Solving for v_{0y}: A QB's Challenge

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In summary, the conversation discusses a quarterback throwing a football to a receiver running at a constant velocity. The quarterback must estimate the angle and time interval for the receiver to catch the ball without opposition players interfering. The problem involves finding the vertical component of the ball's velocity when the quarterback releases it, using the variables t_c and g. The person asking for help is struggling to understand the problem and is looking for relevant equations for projectile motion. They also inquire about how to plot a graph in Matlab showing the relationship between angle and range of a projectile.
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polymerase
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A quarterback is set up to throw the football to a receiver who is running with a constant velocity [tex]v_{r}[/tex] directly away from the quarterback and is now a distance "D" away from the quarterback. The quarterback figures that the ball must be thrown at an angle [tex]\theta[/tex] to the horizontal and he estimates that the receiver must catch the ball a time interval [tex]t_{c}[/tex] after it is thrown to avoid having opposition players prevent the receiver from making the catch. In the following you may assume that the ball is thrown and caught at the same height above the level playing field. Assume that the y coordinate of the ball at the instant it is thrown or caught is y= 0 and that the horizontal position of the quaterback is x= 0.
Use "g" for the magnitude of the acceleration due to gravity, and use the pictured inertial coordinate system when solving the problem.

Find [tex]v_{0y}[/tex], the vertical component of the velocity of the ball when the quarterback releases it. express [tex]v_{0y}[/tex] only in terms of [tex]t_{c}[/tex] and "g"
 

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What have you tried so far? What is causing you trouble?
 
  • #3
hage567 said:
What have you tried so far? What is causing you trouble?

I just don't understand wut its asking...im so use to something like this saying the answer is [tex]v_{0y}[/tex] = sin[tex]\theta[/tex][tex]v_{0}[/tex]
 
  • #4
Don't you have some relevant equations for projectile motion? Hint: take a look at the first item in my footer.
 
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  • #5
Hi
How to plot graph of projectile motion between angle and range in Matlab?
I mean that what will be the coding for the graph between angle and range of any projectile?
 

FAQ: Solving for v_{0y}: A QB's Challenge

How do you determine the initial vertical velocity (v0y) of a quarterback's throw?

The initial vertical velocity of a quarterback's throw can be determined using the equation v0y = vy - gt, where vy is the final vertical velocity, g is the acceleration due to gravity (9.8 m/s2), and t is the time in seconds. This equation assumes that the throw starts and ends at the same height, and that there is no air resistance.

How does the angle of release affect the initial vertical velocity of a quarterback's throw?

The angle of release can greatly impact the initial vertical velocity of a quarterback's throw. The higher the angle of release, the greater the initial vertical velocity will be. This is because a higher angle of release allows for more of the quarterback's throwing motion to be directed vertically, resulting in a higher initial vertical velocity.

Is the initial vertical velocity of a quarterback's throw affected by the ball's weight?

The weight of the ball does not directly affect the initial vertical velocity of a quarterback's throw. However, a heavier ball will require more force to be thrown at the same speed, meaning that a heavier ball may result in a lower initial vertical velocity compared to a lighter ball thrown with the same force.

How does air resistance impact the initial vertical velocity of a quarterback's throw?

Air resistance can greatly affect the initial vertical velocity of a quarterback's throw. As the ball travels through the air, it will experience air resistance, which will slow it down. This means that the initial vertical velocity will decrease over time as the ball travels to its destination.

Does the altitude of the playing field affect the initial vertical velocity of a quarterback's throw?

The altitude of the playing field can affect the initial vertical velocity of a quarterback's throw. This is because the gravitational acceleration (g) is slightly lower at higher altitudes, meaning that the ball will experience slightly less acceleration due to gravity and may have a slightly lower initial vertical velocity compared to a throw at a lower altitude.

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