A motorcycle has a velocity of 15 m/s due south as it passes a car with a velocity of 24m/s due north. What is the magnitude and direction of the velocity of the motorcycle an seen by the driver of the car.
(24+15) m/s south
call north positive
Vmc = -15
Vcar = +24
Vrelative= Vmc - Vcar = -15 - 24 = - 39
39 south
Well, here's a joke for you: Why don't scientists trust atoms? Because they make up everything!
Now, let's tackle your question. When two objects with velocities in opposite directions are considered, we can simply add their velocities together to get the relative velocity.
In this case, the motorcycle has a velocity of 15 m/s due south, while the car has a velocity of 24 m/s due north. To find their combined velocity, we subtract the motorcycle's velocity from the car's velocity:
24 m/s - 15 m/s = 9 m/s
So, when seen by the driver of the car, the magnitude of the velocity of the motorcycle is 9 m/s. As for the direction, it would be in the opposite direction of the car, so we can say the motorcycle's velocity is 9 m/s due north.
Remember, velocity is defined by both magnitude and direction.
To find the magnitude and direction of the velocity of the motorcycle as seen by the driver of the car, we need to apply the concept of relative velocity.
Relative velocity refers to the velocity of an object with respect to another object or observer.
In this case, the motorcycle is moving south with a velocity of 15 m/s, and the car is moving north with a velocity of 24 m/s. Since opposite directions have opposite signs, we can consider the velocities as -15 m/s (southward) for the motorcycle and +24 m/s (northward) for the car.
To find the relative velocity of the motorcycle as seen by the car driver, we subtract the velocity of the car from the velocity of the motorcycle:
Relative Velocity = Velocity of Motorcycle - Velocity of Car
Relative Velocity = -15 m/s - (+24 m/s)
Relative Velocity = -15 m/s - 24 m/s
Relative Velocity = -39 m/s
So, the magnitude of the velocity of the motorcycle as seen by the driver of the car is 39 m/s. However, since the motorcycle is moving south and the car is moving north, the direction will be southward for the car's driver. Therefore, the direction of the velocity is south.
To summarize, the magnitude of the velocity of the motorcycle, as seen by the driver of the car, is 39 m/s southward.