Finding Horizontal Distance in Projectile Motion

[aliceeelu]

Homework Statement

A 0.5kg rock is projected from the edge of the top of a building with an initial velocity of 13.7m/s at an angle 60^o above the horizontal. The building is 6.89m in height . At what horizontal distance, x, from the base of the building will the rick strike the ground? Assume the ground is level and that the side of the building is vertical. The acceleration of gravity is 9.8m/s².

Homework Equations

dy = Voyt + 1/2at^2
Vx = dx/t

The Attempt at a Solution

I have tried to find the vertical and horizontal component of the rock at its highest point. Using the vertical component, I found a time, which would be how long it took for the rock to get to its highest point from its original position. Then, I added the vertical component and the height of the building, and used that as the dy to find the time it takes for the rock to go from its highest point to the ground. I added the two times, and found a dx.

My assignment is a quest on the UTexas site, so it would tell me when my answer is wrong.

And here's a diagram:

Thank you for your help!

 

[Jack21222]

You're making this WAY more complicated than you need to. Did you learn that the x-component of velocity is Vcos $$\theta$$ and the y component of velocity is Vsin $$\theta$$, where theta is the angle made with the x axis?

You're given everything you could possibly want in this problem, just plug and chug.

Edit: To clarify, just write down what you do know. You know y-initial, y-final, x-initial, Vx initial, Vx final, Vy initial, acceleration in the x direction, acceleration in the y direction. The only things you don't know are time, x-final, and Vy-final. You have 3 unknowns and 4 equations (2 for x, 2 for y). Plug and chug.

The way I do every one of these problems is to write down a list of everything you could possibly know about the system. That's 11 items. Initial and final position, initial and final velocity, acceleration, and time. Do that for the x and the y directions. Time is the same, so you only put that down once. After you list those 11 items, fill in what you know, and use that to solve for what you don't.

If you do that, solving for it's highest point, or doing anything fancy like that doesn't even come into play.

 

[tomcue]

Based on the information provided, it seems like you are on the right track in your attempt to find the horizontal distance in projectile motion. To find the horizontal distance, x, from the base of the building where the rock strikes the ground, you will need to use the horizontal velocity, Vx, and the time, t, it takes for the rock to reach the ground.

Using the equations you have mentioned, you can find the time it takes for the rock to reach its highest point and then the time it takes for the rock to reach the ground. After finding these times, you can use the equation Vx = dx/t to find the horizontal distance, x.

In addition, it is important to note that the vertical and horizontal components of the rock's initial velocity can be found using trigonometric functions. For example, the vertical component would be V0sin(60) and the horizontal component would be V0cos(60).

I hope this helps and good luck with your assignment!