How far does the object travel horizontally? Two-Dimensional Motion

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A rifle bullet is fired from a cliff at an angle of 30° below the horizontal with an initial velocity of 800 m/s from a height of 80 m. To determine the horizontal distance traveled, the vertical motion must first be analyzed to find the time of flight. The vertical velocity component is calculated as 400 m/s, and the time can be derived using the equation for vertical motion. Once the time is known, it can be used to calculate horizontal distance using the horizontal velocity component. Understanding the relationship between vertical and horizontal motion is crucial for solving this two-dimensional motion problem.
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Homework Statement


A rifle bullet is fired from the top of a cliff at an angle of 30° below the horizontal. The initial velocity of the bullet is 800 m/s. If the cliff is 80 m, high, how far does it travel horizontally?

θ = 30°
v0 = 800 m/s
y = 80 m


Homework Equations


I may be totally off here with these equations (I'm part of an independent study program and their physics curriculum doesn't even have an online teacher, so I've been flying blind since day one), but I think these are relevant:

vy = Vsinθ
|v| = √vx2 + vy2

The Attempt at a Solution


vy = 800sin30 = 400

800 - 400 = 400 = vx

I then thought I could go from there to solve for x using x = x0 + v0xt + 1/2at2, but I don't have anything for t, so I'm stuck.
 
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With 800 - 400 = 400 = vx you got the right answer, but only accidentally. To get the correct answer the correct way, you must use the second equation you listed in the relevant eq-s section.

Before you you compute the horizontal distance, ask yourself how far the bullet will travel vertically. And how long that will take.
 
I actually was using the equation I listed in the relevant eq-s section, but I do see how that isn't entirely clear.

I unfortunately really do not know where to go from where I'm at. The bullet will travel 80 m vertically, yes? But I don't understand how to use any of that to help me get time.

Could I use y = y0 + v0t to find out time, or does that not work here?
 
Last edited:
eioz said:
The bullet will travel 80 m vertically, yes? But I don't understand how to use any of that to help me get time.

The distance of vertical travel depends on the initial vertical velocity, acceleration and time. You know all of these except the time, so you should be able to find it.
 
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