QB Throws Football: Speed, Angle, & Distance Needed to Catch

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Homework Help Overview

The problem involves projectile motion, specifically analyzing the trajectory of a football thrown by a quarterback. The scenario includes determining the speed at which a receiver must run to catch the football, given its initial speed, launch angle, and the distance between the quarterback and the receiver.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relevant equations for projectile motion, focusing on both horizontal and vertical components. There is an attempt to relate the range of the projectile to the receiver's required speed and the time of flight. Questions arise regarding the definitions of variables used in the equations.

Discussion Status

The discussion is ongoing, with participants exploring the relationships between the variables involved in the problem. Some guidance has been provided regarding the equations needed for analysis, and there is a clarification of the variable representing the horizontal distance covered by the projectile.

Contextual Notes

Participants are working within the constraints of the problem setup, including the initial conditions provided and the requirement for the receiver to catch the football at the same height from which it was thrown.

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a quaterback throws a football towards a reciever with an initial speed of 22m/s, at an angle of 34 degrees above the horizontal. At that instant, the reciever is 21 m from the quarterback. The acceleration of gravity is 9.8 m/s ^2. WIth what constant speed should the reciever run in order to catch the football at the level at which it was thrown? Answer in units of m/s.
 
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What are the important equations for projectile motion? There should be two you should be using, one for the horizontal direction and one for the vertical.
 
Applying the equations determine range R and time of flight T of the football. To catch the football, the reciever must cover a distance (21 - R) m in time equal to time of flight T. Speed of reciever = (21-R)/T.
 
what does the variable R represent?
 
R represents the horizontal distance covered by the projectile.
 

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