# How do I calculate the deflection angle in a bowling split conversion?

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In summary, the conversation discusses the calculation of the deflection angle in bowling when converting a tough split. It is necessary to strike the pin at a glancing blow, and the collision is assumed to be elastic and without spin. The initial speed of the ball and mass of the pin are given, and parts A and B have already been calculated. The individual is seeking guidance on how to calculate the deflection angle and options include using conservation of momentum or drawing a resultant triangle. The use of the law of cosines is also mentioned.
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[SOLVED] Deflection Angle

Hey guys, back again lol, got a really quick question:

In order to convert a tough split in bowling it is necessary to strike the pin a glancing blow as shown. Assume that the bowling ball, initially traveling at 12.0 [m/s], has five times the mass of the pin and that the pin goes off at 80[degrees] from the original direction of the ball. Calculate the speed A) of the pin and B) of the ball just after collision and C) calculate the angle through which the ball as deflected. Assume the collision is elastic and ignore any spin of the ball.

So far I've done part A and part B, but I'm ashamed to say I'm having trouble calculating the angle. Do I make a resultant triangle? A point in the right direction would be great

^ ^ thank you!

Return

Hi Return!

You know all three speeds, and one angle, whic is more than enough information … you can use conservation of momentum in the original direction of the ball, or perpendicular to it, or you can draw a resultant triangle.

So if I want to use the velocities, I use the law of cosines right?

law of cosines?

if you mean that the component of a vector (like a velocity or a force) in a particular direction is the value of the vector times the cosine …
… then yes!

## What is deflection angle?

Deflection angle is the angle between the original direction of an object and the direction it takes after being deflected by an external force or field.

## How is deflection angle measured?

Deflection angle is typically measured using instruments such as a protractor, theodolite, or laser tracker. It can also be calculated using trigonometric functions and measurements of distance and displacement.

## What factors affect deflection angle?

Several factors can affect deflection angle, including the magnitude and direction of the external force or field, the distance of the object from the source of the force, and the shape and properties of the object itself.

## What is the relationship between deflection angle and elasticity?

Deflection angle is directly related to the elasticity of an object. Objects with higher elasticity will experience a smaller deflection angle when subjected to the same external force compared to objects with lower elasticity.

## How is deflection angle used in engineering and physics?

Deflection angle is an important concept in engineering and physics, as it allows for the prediction and control of the behavior of objects under external forces. It is commonly used in the design of structures, machinery, and other systems to ensure their stability and functionality.

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