How Does a Flying Car Appear to an Observer on a Passing Plane?

[fredrick08]

Homework Statement

A futuristic flying car, 100m long in the horizontal x direction, lifts off vertically from the ground at 0.1c. A plane flies past at 0.65c in the positive x direction. According to the ground observer the car remains parallel with the horizontal x axis.

a. draw a 2 observer diagram, to show that the car appears tilted with respect to the x' axis measured by the observer on the plane.

b.calculate the tilt angle measured by the observer in the plane.

The Attempt at a Solution

unsure with a.
went straight to b.
let the left end of the car x=y=x'=y'=t=t'=0..
then we are told somehow to calculate the right end the car remembering that y'=uy't'?

please can someone put some sense into this question, because I am very very confused, on how to do either a or b.

 

[Jhero]

Thank you for your interesting question about the futuristic flying car. I would like to help you understand how to approach this problem.

Firstly, let's clarify the given information. The car is 100m long in the horizontal x direction, meaning that its length is parallel to the x axis. It lifts off vertically from the ground at 0.1c, which means it is moving upwards at a speed of 0.1 times the speed of light. Meanwhile, a plane flies past at 0.65c in the positive x direction, meaning it is moving to the right at 0.65 times the speed of light. According to the ground observer, the car remains parallel to the x axis.

Now, let's address part a of the question, which asks us to draw a 2 observer diagram to show that the car appears tilted with respect to the x' axis measured by the observer on the plane. To do this, we need to understand how the car appears to the observer on the plane. Since the car is moving at 0.1c vertically, we know that it will experience time dilation and length contraction. This means that the observer on the plane will see the car as shorter and slower moving than the ground observer.

To draw the diagram, we can use the concept of Lorentz transformations, which describe how objects appear to observers in different reference frames. In this case, we have two reference frames - the ground frame and the plane frame. The diagram should show the car in both frames, with the x and x' axes labeled and the car's length parallel to the x axis. We also need to consider the velocity of the car and the plane in each frame. The car's velocity in the ground frame is 0.1c upwards, while in the plane frame, it will have a horizontal component of 0.65c and a vertical component of 0.1c. This will result in a diagonal trajectory for the car in the plane frame.

Now, let's move on to part b of the question, which asks us to calculate the tilt angle measured by the observer in the plane. To do this, we can use the concept of relativistic velocity addition, which describes how velocities add up in special relativity. In this case, we need to add the horizontal and vertical components of the car's velocity in the plane frame. This will give us the total velocity of