# Speed of an object relative to another

• ilovejava
In summary, the question involves calculating the relative speed of two protons in a colliding beam apparatus. Using the formula u'=(u-v)/(1-(uv/c2)), the speed of the second proton relative to the first is 0.136c. This was calculated by plugging in the speeds of the two protons (-0.86c and 0.82c) and taking the absolute value of the second proton's speed.
ilovejava

## Homework Statement

In a colliding beam apparatus, two beams of protons are aimed at each other. The first proton moves with a speed of 0.82c to the right; the second moves with a speed of 0.86c to the left. Both speeds are measured relative to the laboratory frame of reference. What is the speed of the second proton relative to that of the first?

## Homework Equations

u'=(u-v)/(1-(uv/c2))

## The Attempt at a Solution

u = speed of second object -0.86c
v = speed of first object +0.82c

Plugging into the equation u and v I get -1.68C but this doesn't make sense. So, what I did was just take the absolute value of the speed of the second object (0.86c) and now plugged this new value and got u' = 0.136c . Did I approach this problem correctly?

Thanks.

Last edited:
You just did the algebra wrong. Try again to calculate:
$$\frac{-0.86 - 0.82}{1-(-0.86)*(0.82)}$$

## 1. What is the definition of relative speed?

The relative speed of an object is the rate at which it is moving with respect to another object. It takes into account the motion of both objects and their direction of movement.

## 2. How is relative speed calculated?

Relative speed is calculated by subtracting the velocity of one object from the velocity of another. The result is the speed at which one object is moving with respect to the other.

## 3. Does the relative speed between two objects change?

Yes, the relative speed between two objects can change depending on their motion and direction. For example, if two cars are moving towards each other, their relative speed will decrease as they get closer. On the other hand, if they are moving away from each other, their relative speed will increase.

## 4. Can two objects have the same relative speed?

Yes, it is possible for two objects to have the same relative speed. This can occur if they are both moving at the same velocity in the same direction.

## 5. How does the speed of an observer affect relative speed?

The speed of an observer does not affect the relative speed between two objects. The relative speed is only dependent on the velocities of the objects in relation to each other.

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