Relative motion!

Question

1.) Bob is standing at the side of the road. Sue is standing in a bus. Bob measures the bus to be traveling

North at a speed of 30.0 m/s. Sue is holding a ball 10.0 meters above the floor of the bus. She then drops the ball (assume the only force acting on the ball is the force of gravity). What is the speed of the ball 1.00 second after the ball is released as measured by Sue? What is the speed of the ball 1 second after the ball is released as measured by Bob?

2.) A helicopter travels with an air speed of 55 m/s. The helicopter heads in the direction [W35oN]. What is velocity relative to the ground if the wind velocity is

1. a) 21 m/s [E]
2. b) 21 m/s [N 22oW]?

3.) While you are vacationing in Hawaii, you spot a plane traveling in the direction [60.0o S of E]. If its ground velocity is 210.0 km/h and the wind speed is 150.0 km/h [south], what is the plane’s velocity relative to the air? Draw a diagram.

Answer 1

Since Sue is inside the bus, from her perspective, the bus looks like it is at rest although it is moving. When she drops the ball, from her perspective, it will appear to be simply moving vertically downwards. So, one second after it is dropped, the relative velocity of the ball as measured by Sue is the acceleration due to gravity times 1 second. So it is 9.8m/s².

As far as Bob is concerned, the ball will have two different velocities, the downward velocity and the horizontal velocity of the bus. Since these two velocities are perpendicular, the magnitude of the resultant velocity will be

v=√(9.8²+30²)=31.56m/s