Frames of reference and relative velocity

[paultt]

I am in desperate need of help with a certian physice question I am struggling on. here's the question:

"A pilot is required to fly directly from london to rome, in 3.5hours. the displacement is 1400km [S 43degrees E]. a wind is blowing with a velocity of 75km/h [E]. what is the required velocity of the plane relative to the air."


-if anyone who knows the full solution it would be great.

 

[Hargoth]

Reformulate the question: How fast does the plane go when it's in the air with it's motor switched off (supposed it goes with the wind and doesn't fall down)? How much speed does the motor have to "add"?

 

[kyle8921]

I can provide an explanation of frames of reference and relative velocity to help you understand and solve this problem.

Frames of reference refer to the point or system from which measurements are taken. In this case, we can consider the plane as one frame of reference and the ground as another. The pilot's goal is to reach Rome, which is a specific point in the ground frame of reference, in a given time of 3.5 hours.

Relative velocity is the velocity of an object with respect to another object. In this case, the required velocity of the plane relative to the air is the velocity needed for the plane to move in the direction of Rome, while taking into account the wind's velocity.

To solve this problem, we can use vector addition to find the required velocity. The displacement of the plane is given as 1400km [S 43degrees E]. This means that the plane needs to travel 1400km in the direction of south 43 degrees east. We can break this displacement into two components: one in the east direction and one in the south direction.

The wind is blowing with a velocity of 75km/h [E], which means it is blowing in the east direction. This wind velocity is the same in both frames of reference. We can use this information to find the east component of the required velocity.

To find the south component, we can use trigonometry and the given displacement to find the angle between the displacement and the south direction. This angle is equivalent to the angle between the required velocity and the south direction. We can then use trigonometric functions to find the south component of the required velocity.

Once we have both components, we can use vector addition to find the magnitude and direction of the required velocity. This will give us the velocity of the plane relative to the air, which is what the pilot needs to reach Rome in 3.5 hours.

In conclusion, frames of reference and relative velocity are important concepts in physics that help us understand the motion of objects in relation to other objects. By using vector addition and trigonometry, we can solve problems involving different frames of reference and find the required velocity of an object relative to another object. I hope this explanation helps you in solving the given problem.