How far must the quarterback throw the ball?

[Crusaderking1]

Homework Statement

At Enormous State University (ESU), the football team records its plays using vector displacements, with the origin taken to be the position of the ball before the play starts. In a certain pass play, the receiver starts at +2.0 {i} - 5.0 {j}, where the units are yards, {i} is to the right, and {j} is downfield. Subsequent displacements of the receiver are +9.0 {i}(in motion before the snap), +10 {j}(breaks downfield), - 6.0{i}+ 4.0 {j}(zigs), and +12.0{i} + 18.0 {j} (zags). Meanwhile, the quarterback has dropped straight back to a position - 7.0 {j}.How far must the quarterback throw the ball?


In which direction must the quarterback throw the ball?

Homework Equations

Probably R_x+R_y=R

The Attempt at a Solution

I drew the diagram.

Do I have to use two triangles to figure this out, then add those vectors, or something? I would find the components but I don't have any angles to work with(that I know of).

Did you guys have the receiver end on coords (17,27) and the QB on coords(0,-7)?

(17)^2+(34)^2, then square root = 38.0 yards
tan-1 (34/17) = 90-63.43 = 26.5 degrees to right of downfield.

Is that right for yards. Doesn't seem right.
Thanks!

 

[NewtonianAlch]

What's the question?

 

[Crusaderking1]

How far must the quarterback throw the ball?In which direction must the quarterback throw the ball?

 

[Crusaderking1]

Alright, I figure out this is correct.

 

[rwisz]

I would approach this problem by first understanding the given information and the goal of the problem. From the given information, we can see that the receiver starts at a position of +2.0 {i} - 5.0 {j}, which means they are 2 yards to the right and 5 yards downfield from the origin (the position of the ball before the play starts). The subsequent displacements of the receiver show that they move in various directions before ending up at the coordinates (17, 27).

To determine how far the quarterback must throw the ball, we need to find the distance between the receiver's final position and the quarterback's position, which is -7.0 {j}. This can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the distance between the two positions) is equal to the sum of the squares of the other two sides (in this case, the x and y components of the distance). So we can set up the equation as follows:

d^2 = (17 - 0)^2 + (27 - (-7))^2

where d is the distance between the receiver and the quarterback. Simplifying, we get:

d^2 = 17^2 + 34^2

d^2 = 289 + 1156

d^2 = 1445

d = √1445

d = 38.0 yards

So the quarterback must throw the ball a distance of 38.0 yards to reach the receiver's final position.

As for the direction in which the quarterback must throw the ball, we can use trigonometry to calculate the angle between the line connecting the receiver's final position and the quarterback's position and the downfield direction. We can use the tangent function to find this angle, which is defined as the opposite side (in this case, the distance between the two positions) divided by the adjacent side (in this case, the distance in the x direction between the two positions). So we can set up the equation as follows:

tanθ = (27 - (-7)) / (17 - 0)

tanθ = 34 / 17

θ = tan^-1 (34 / 17)

θ = 63.43 degrees

This means that the quarterback must throw the ball at an angle of 63.43 degrees to the right of the downfield