A railroad flatcar is traveling at the speed of 13.0 m/s relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar. What is the velocity(magnitude and direction)of the motor scooter relative to the flatcar if its velocity relative to the observer on the ground is
a) 8.0 m/s to the right?
b) 2.0 m/s to the left?
c) zero?
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To solve this problem, we'll need to understand the concept of relative velocities.
Relative velocity is the velocity of an object as observed from another reference frame. In this case, we have an observer on the ground, the flatcar, and the motor scooter. We need to find the velocity of the motor scooter relative to the flatcar.
Let's solve each part of the problem step by step:
a) When the motor scooter is moving 8.0 m/s to the right relative to the observer on the ground, we need to find its velocity relative to the flatcar.
To do this, we can use the subtraction method. Subtract the velocity of the flatcar (13.0 m/s) from the velocity of the motor scooter relative to the observer on the ground (8.0 m/s to the right).
Velocity of the motor scooter relative to the flatcar = Velocity of the motor scooter relative to the observer - Velocity of the flatcar
= 8.0 m/s to the right - 13.0 m/s
= -5.0 m/s to the left
So, the velocity of the motor scooter relative to the flatcar is 5.0 m/s to the left.
b) When the motor scooter is moving 2.0 m/s to the left relative to the observer on the ground, we can apply the same method.
Velocity of the motor scooter relative to the flatcar = Velocity of the motor scooter relative to the observer - Velocity of the flatcar
= 2.0 m/s to the left - 13.0 m/s
= -11.0 m/s to the left
So, the velocity of the motor scooter relative to the flatcar is 11.0 m/s to the left.
c) When the motor scooter has zero velocity relative to the observer, it means it is at rest with respect to the ground. In this case, as the flatcar is moving with a velocity of 13.0 m/s, the motor scooter will also have a velocity of 13.0 m/s in the same direction.
So, the velocity of the motor scooter relative to the flatcar is 13.0 m/s to the right.
In summary:
a) The velocity of the motor scooter relative to the flatcar is 5.0 m/s to the left.
b) The velocity of the motor scooter relative to the flatcar is 11.0 m/s to the left.
c) The velocity of the motor scooter relative to the flatcar is 13.0 m/s to the right.