# 2D Kinematics Problem involving subtended angle

• RjD12
In summary: So, you can equate the two expressions for time, which each give distance travelled from the hill base x and y. Also, the slope of the hill is used to express the y distance as a function of x.
RjD12

## Homework Statement

Mortar crew is near the top of a steep hill. They have a mortar. They angle this mortar at an angle of $\theta$ = 65° . The crew fires a shell at a muzzle velocity of 228 ft/sec (69.5 m/s). How far down the hill does the shell strike if the hill subtends an angle of $\phi$ = 32° from the horizontal?

How long will the mortar remain in the air?
How fast will the shell be traveling when it hits the ground?

Relevant diagram: http://imgur.com/apimguh

## Homework Equations

Kinematic Equations:

X= Xo + Voxt

Y= Yo + Voyt - (1/2)at2

## The Attempt at a Solution

First off, I'm not expecting to get all of my questions answered. I just need a little push.

I'm not sure where to start off at here. The fact that there are two angles here confuses me in regards to how they work in the equations.

I can say that Vox = 69.5cos(65) and that Voy = 69.5sin(65).

I'm really thrown off by the way the angles work here, and whether the distance works with a simple range equation. Any tips on where to start?

edit: Additionally, I was given the equation d = Vo + (1/2)at2 as a hint for this. Isn't this wrong though, seeing as how the velocity should be multiplied with time?

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I'll start you off:

A "mortar" in this example refers to the mortar tube or gun depending on the period.
Think of it as a kind of cannon. Draw a dot on your page to represent the position of the mortar.

The mortar is sitting on the side of a hill.
The hill has a slope - given as below the horizontal.
So draw in a (dotted) horizontal line through the mortar and figure out which way is "below" - measure the angle in that direction and draw in a bold line through the mortar indicating the slope of the hill.

The angle of the mortar is above the horizontal - you know how to do that right?
So draw an arrow for the initial velocity v at the correct angle.

The mortar shell will go in a parabola until it hits the side of the hill - which keeps going down at the same angle.

You should be able to take it from there.

Strange that the picture seems to have been posted before Simon commented. It looks excelent.
I checked your earlier thread and I think you only need a small nudge.

The hint you got is suspicious, because d = Vo + (1/2)at2 is dimensionally incorrect -- as you note. Kinematic relations are OK. Look at them in a math fashion: you still have three unknowns (x, y, t) so something else is needed (for example, in flatland: y(t)=0 when poof).

In this exercise it is the slope of the hill, that provides you with a relationship between X(t) and Y(t) at boom time. If you express it deftly in terms of d and ##\phi## you end up with only two unknowns (d and t_strike) in two equations. Bob's your uncle...

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Hmmm... looks like I didn't see it.
Either that or it was edited in while I was doing something else.
I don't think I took a half-hour to type the reply but I sometimes have several threads up in different tabs.

Looking at the diagram:
Basically the projectile ends up at a different height than it started at - this height depends on the horizontal distance traveled.

You could think of it as the intersection of a parabola with a line - do you know how to get the gradient of a line from the slope angle?

Once you have the (x,y) coordinates of the endpoints you can get d.

I had a more elaborate hint but I'll reinforce BvU at this point :)

It is 2D Kinematics. The time for the shell to reach horizontally at D(x) is equal to time it reaches D(y).

## 1. What is a subtended angle in 2D kinematics?

A subtended angle in 2D kinematics is the angle between two vectors that originate from the same point. It is often used to describe the angle between an object's initial and final position in 2D motion.

## 2. How is a subtended angle calculated in 2D kinematics?

In order to calculate the subtended angle in 2D kinematics, you can use the dot product formula: θ = cos^-1((a*b)/(|a||b|)), where a and b are the two vectors originating from the same point and |a| and |b| represent the magnitudes of those vectors.

## 3. What is the significance of a subtended angle in 2D kinematics?

A subtended angle in 2D kinematics is significant because it allows us to analyze the direction and magnitude of an object's motion. It can also be used to calculate the displacement and velocity of an object in 2D motion.

## 4. How does the magnitude of a subtended angle affect an object's motion in 2D kinematics?

The magnitude of a subtended angle can affect an object's motion in 2D kinematics in two ways. Firstly, a larger subtended angle indicates a greater change in direction for the object, resulting in a larger displacement. Secondly, the magnitude of the subtended angle can affect the velocity of the object, as a larger angle can result in a higher velocity.

## 5. Can a subtended angle be negative in 2D kinematics?

Yes, a subtended angle can be negative in 2D kinematics. This occurs when the two vectors originating from the same point are in opposite directions, resulting in a negative dot product. In this case, the angle will be measured in the opposite direction from the positive angle.

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