# Triangle Problem Homework: Solving for Ball Speed After Collision

• Fusilli_Jerry89
In summary, the bowling ball has a mass of 3.2 kg and is moving west at 4.2 m/s when it collides with a stationary ball of mass 3.2 kg. The first ball's speed is 1.7 m/s after the collision.
Fusilli_Jerry89

## Homework Statement

A bowling ball mass 3.2 kg rolls west at 4.2 m/s striking a stationary ball mass 3.2 kg. After the collision the second ball travels in a direction 24 degrees south of west at 3.6 m/s. Whats the first balls speed after the collision.

mv+mv=mv+mv

## The Attempt at a Solution

p1=13.44 kgm/s W
p2=0
p1'=?
p2'=11.52 kgm/s 24 degrees south of west

13.44 W - 11.52 24 S of W = p1'
I then drew the resulting vectors and subtracted them getting a triangle with the lengths 13.44, 11.52, and 5.52 with an angle of 24 degrees between 13.44 and 11.52. My question is that when i use sine law to get the two remaining angles, all the angles only add up to 160 degrees. What's the deal here? (I got the length of the last angle via: x^2=13.44^2+11.52^2-2(13.44)(11.52)cos24)

Fusilli_Jerry89 said:
(I got the length of the last angle via: x^2=13.44^2+11.52^2-2(13.44)(11.52)cos24)

You probably meant, you got the length of the third side of the triangle, i.e. x should represent the magnitude of the momentum vector p1', which, divided by the mass m1 = 3.2, gives the magnitude of the velocity.

k that's what i meant the length of the last side, but when I use sine law to find out the 2 remaining angles, they all do not add up to 180

Fusilli_Jerry89 said:
k that's what i meant the length of the last side, but when I use sine law to find out the 2 remaining angles, they all do not add up to 180

Why are you trying to find the angle? Don't you have to find the speed only? If so, as said, you only have to divide that 'third' triangle side by the mass, since it represents momentum.

Yes, but I am curious as to why the angles to not make sense. I donno about u but just knowing that the triangle i drew duznt make any sense wuld make me wonder if i even did it right? Ne ways i got 1.7 m/s

Fusilli_Jerry89 said:
Yes, but I am curious as to why the angles to not make sense. I donno about u but just knowing that the triangle i drew duznt make any sense wuld make me wonder if i even did it right? Ne ways i got 1.7 m/s

Your answer is correct. I got the angles right, but I wouldn't worry about that if I were you.

k but if it asked for the angle at which it went, how wuld u do that?

nm i figured it out but instead using a dfferent method

Fusilli_Jerry89 said:
k but if it asked for the angle at which it went, how wuld u do that?

There is nothing wrong with graphical solutions, but they are not the most accurate way to solve such a problem. The most accurate approach is to resolve the known vectors into components using trigonometric ratios, and solve for the components of the unknown vectors.

Set up a coordinate system with x and y axes overlaying the compass directions, with +y going North and +x going East. Write your known vectors in terms of x and y components and use conservation of momentum to find the components of the third vector. Once you have the components, find the magnitude of the vector and its direction. I know you don't need the direction for this problem, but you said you wanted to get it right.

yeah i just figured that out right after i posted this, i was just wonder why the triangle didnt make any sense it all. I see how it culdnt make sense, but I guess trig duznt always make sense?

## 1. What is the "Triangle Problem" in relation to solving for ball speed after collision?

The "Triangle Problem" refers to a common physics problem where the motion of a ball after a collision is determined by using the law of conservation of momentum and the law of conservation of energy. The problem is typically represented by a triangle, with the ball's initial velocity, final velocity, and the velocity of the target or other object involved in the collision.

## 2. How do you solve for ball speed after collision in the "Triangle Problem"?

To solve for ball speed after collision in the "Triangle Problem", you would first need to gather information about the initial velocity and mass of the ball, as well as the velocity and mass of the target or other object. Then, you would use the equations for conservation of momentum and conservation of energy to determine the final velocity of the ball after the collision.

## 3. What are the key concepts involved in solving the "Triangle Problem" for ball speed after collision?

The key concepts involved in solving the "Triangle Problem" for ball speed after collision include conservation of momentum, conservation of energy, and the equations for calculating these principles. Additionally, an understanding of basic trigonometry and vector mathematics may also be necessary to accurately solve the problem.

## 4. How does the "Triangle Problem" relate to real-world scenarios?

The "Triangle Problem" has applications in real-world scenarios involving collisions, such as in sports (e.g. calculating the speed of a pitched baseball after colliding with a bat) or in car accidents (e.g. determining the speed of a car after colliding with another car). It is also used in engineering and physics to analyze the behavior of objects in motion.

## 5. Are there any limitations or assumptions when solving the "Triangle Problem" for ball speed after collision?

Yes, there are limitations and assumptions when solving the "Triangle Problem" for ball speed after collision. Some of these include assuming that the collision is elastic and that there are no external forces acting on the objects. Additionally, the problem may become more complex if there are multiple objects involved in the collision or if there is friction present. Real-world scenarios may also have other factors that need to be considered, such as air resistance.

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