Projectile Motion — How far from the gun does the bullet land?

[Tinkylo]

Homework Statement

The bullet fired from a gun on the ground has a velocity v. The x-component of the velocity is 8.4 ms-1 and the y-component of the velocity is 9.2 ms-1. x is the horizontal axis and y is the vertical axis. What is the distance in m between the gun and the point where the bullet hits the ground? Acceleration due to gravity is 9.8ms-2. Assuming there is no air resistance during the bullet's flight.

Relevant Equations

Not sure

I don't know how to link the x-component and y-component together.

 

[haruspex]

I don't know how to link the x-component and y-component together.

Distance, start velocity, final velocity, time, acceleration. For which does the same value apply to both coordinates?

 

[ehild]

I don't know how to link the x-component and y-component together.

As there is no air resistance, the vertical and horizontal components of velocity are not linked in the problem.Consider the problem as independent horizontal and vertical motions.

 

[Lnewqban]

Relevant Equations:: Not sure

I don't know how to link the x-component and y-component together.

Don't link those, they are giving you the vertical and horizontal components of the initial velocity in order to facilitate the problem.
Hits:
Purely vertical movement: decelerated while moving up / stop / accelerated while falling down.
Purely horizontal movement: non-accelerated and lasting as much as the up-down vertical movement.

 

[haruspex]

Don't link those

It's not clear what @Tinkylo means by linking them. My interpretation is finding something that links the horizontal and vertical equations. See my hint in post #2.

 

[Andrew Mason]

Homework Statement:: The bullet fired from a gun on the ground has a velocity v. The x-component of the velocity is 8.4 ms-1 and the y-component of the velocity is 9.2 ms-1. x is the horizontal axis and y is the vertical axis. What is the distance in m between the gun and the point where the bullet hits the ground? Acceleration due to gravity is 9.8ms-2. Assuming there is no air resistance during the bullet's flight.
Relevant Equations:: Not sure

I don't know how to link the x-component and y-component together.

You can work it out from first principles from the equations for x and y as a function of t (time). This involves finding the value of t when y = 0 and then using that value of t in the equation for x. Or you can use the relationship between range, velocity and launch angle that you may have been given: $R = \frac{v_0^2 \sin{2\theta}}{g}$. If you use this relationship, you will have to find $v_0$ and the launch angle. Which method do you wish to use?

AM