Question

A girl stands on a moving sidewalk (conveyor belt) that is moving to the right at a speed of 2 m/s relative to the ground. A dog runs on the belt toward the girl at a speed of 8 m/s relative to the belt. 1) what is the speed of the dog relative to the ground?

Answer 1

The speed of the dog relative to the ground is the sum of its speed relative to the moving sidewalk and the speed of the sidewalk itself, which results in 10 m/s to the right.

Step-by-step explanation:

To determine the speed of the dog relative to the ground, we need to consider the relative velocity concept. If the moving sidewalk (conveyor belt) moves to the right at a speed of 2 m/s and the dog runs toward the girl at a speed of 8 m/s relative to the belt, then the speed of the dog relative to the ground is the sum of these two speeds because they are in the same direction. Hence, the speed of the dog relative to the ground is:

• Speed of the dog relative to the belt = 8 m/s
• Speed of the belt relative to the ground = 2 m/s
• Total speed of the dog relative to the ground = 8 m/s + 2 m/s = 10 m/s to the right.

The answer to the question is that the speed of the dog relative to the ground is 10 m/s to the right.

Answer 2

To calculate the speed of the dog relative to the ground, we use the formula,

`v_(dog,ground) = v_(dog, belt) + v_(belt, ground)`

Here,
`v_(dog,ground)` is velocity of dog with respect to ground,
`v_(dog, belt)` is velocity of dog with respect to belt and
`v_(belt, ground)` velocity of belt with respect to ground.

Given ,
`v_(dog, belt) = -8 m/s` and
`v_(belt, ground) = 2 m/s`.

Substituting these values in above equation, we get

`v_(dog,ground) = (-8 m/s) + 2m/s = -6 m/s`