# Calculate Change in Momentum of Mass m Launched at 45° Angle

• Victorian91
In summary, the object's final velocity is the same as its initial velocity, but it is pointing downwards.
Victorian91

## Homework Statement

An object of mass m is launched at speed v from point P on horizontal ground at an angle of elevation of 45 degrees, as shown in the picture. When the object reaches point Q the magnitude of the change in momentum of the object is ?

## Homework Equations

Change in momentum of the object
mv - mu

## The Attempt at a Solution

Honestly, I really don't know how to start
All i know is use the formula of the change of momentum
But then the angle 45 degrees I really don't know where to put..
Can somebody help me

Sorry for not attempting
Is because I am a bit blur..
Lastly the options for this question is

A : Zero
B : 1/2 mv
C : 2mv
D : 4mv

Thanks so much..

#### Attachments

• Untitled.jpg
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Okay i think I might be able to solve it..
Finally I manage to attempt this question..

Initial velocity, v = ( vcos45 )^2 + ( vsin45 )^2 ( using pythagorean theorum ) ( to find the resultant velocity
Therefore initial velocity = v
Hence, initial momentum, p =mv

Final velocity, v is the same in magnitude but opposite direction,
Hence final momentum, p =-mv

Hence, change in momentum,
is -mv -mv

=-2mv

But the question just wants the magnitude,
Hence = 2mv

Can anybody tell me whether my working is correct??
Thanks

Victorian91 said:
Final velocity, v is the same in magnitude but opposite direction,

Really? Why do you think that?

Also, momentum is a vector:

$$\Delta\vec{p}=\vec{p}_f}-\vec{p}_i=m\vec{v}_f}-m\vec{v}_i$$

What force is causing the momentum to change? Which direction does this force act in? Hence, which component(s) of the momentum change?

The final velocity of the object will be pointing downwards..
Hence, the it will be the same magnitude as the initial velocity but pointing downwards..

That is what I think..

Or are there any other answers..

Thanks

## 1. What is the formula for calculating change in momentum?

The formula for calculating change in momentum is: p = m * v, where p is the momentum, m is the mass, and v is the velocity.

## 2. How do you calculate the change in momentum of a mass launched at a 45° angle?

To calculate the change in momentum of a mass launched at a 45° angle, you can use the formula: p = m * v * sin(θ), where p is the momentum, m is the mass, v is the velocity, and θ is the angle of launch. Remember to convert the angle to radians if necessary.

## 3. Can you explain the concept of momentum and why it is important?

Momentum is a measure of an object's motion, determined by its mass and velocity. It is important because it helps us understand how objects move and interact with each other. It is also a conserved quantity, meaning it remains constant unless acted upon by an external force. This makes it a useful concept in many fields, including physics and engineering.

## 4. How does the angle of launch affect the change in momentum?

The angle of launch affects the change in momentum because it determines the direction of the object's velocity. A 45° angle, for example, will result in a change in momentum that is equal to the mass times the velocity times the sine of 45°. A greater angle will result in a greater change in momentum, while a smaller angle will result in a smaller change in momentum.

## 5. Are there any other factors that can affect the change in momentum in addition to the angle of launch?

Yes, there are other factors that can affect the change in momentum. These include the mass of the object, the initial velocity, and any external forces acting on the object. The direction and magnitude of these external forces can also impact the change in momentum. Additionally, factors such as air resistance and friction can also affect the change in momentum of an object launched at an angle.

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