Pregunta
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Car A is moving due north at and car B is moving west of north at
. Calculate:
a) The velocity and direction of A relative to B.
b) The velocity and direction of B relative to A.
Two cars simultaneously pass a fork in a road. Car A travels north-east at
and car B travels west at . Calculate the velocity of car A relative to car B in
magnitude and direction.
Car A travels at due north while car B travels due east. If the velocity of car A
relative to car B is , calculate the velocity of car B.
A train is travelling due east at . The velocity of an aeroplane relative to the train
is north. Calculate the actual velocity and direction of the aeroplane.
After a warship fires a torpedo due west at , the ship sails
at . Calculate the velocity of the torpedo a cigar-shaped
relative to the ship.

Ask by Norris Rogers. in South Africa
Jan 25,2025

Solución de tutoría real

Respuesta verificada por el tutor

Responder

Part 1: Velocity of Car A relative to Car B
  • Magnitude: Approximately 88.83 km/h
  • Direction: 13.2° east of north
Part 2: Velocity of Car B relative to Car A
  • Magnitude: Approximately 88.83 km/h
  • Direction: 13.2° south of west
Part 3: Velocity of Car A relative to Car B
  • Magnitude: Approximately 240.4 km/h
  • Direction: 20.5° north of east
Part 4: Velocity of Car B
  • Magnitude: Approximately 94.5 km/h
  • Direction: Approximately 180° (due west)

Solución

To solve the problem, we will break it down into parts as specified.

Part 1: Velocity of Car A relative to Car B

Given:
  • Velocity of Car A, (due north)
  • Velocity of Car B, at west of north.
Step 1: Resolve the velocity of Car B into components.
  • The northward component of Car B’s velocity:
  • The westward component of Car B’s velocity:
Thus, the velocity of Car B in component form is:
Step 2: Calculate the relative velocity of A with respect to B.
Step 3: Calculate the magnitude and direction of .
  • Magnitude:
  • Direction (angle with respect to north):

Part 2: Velocity of B relative to A

Using the same relative velocity concept:
Magnitude:
Direction:

Part 3: Velocity of Car A relative to Car B

Given:
  • Car A travels northeast at .
  • Car B travels west at .
Step 1: Resolve Car A’s velocity.
  • North-east means from both axes:
Thus, the velocity of Car A in component form is:
Step 2: Calculate the relative velocity of A with respect to B.
Step 3: Calculate the magnitude and direction of .
  • Magnitude:
  • Direction:

Part 4: Velocity of Car B

Given:
  • Car A travels at due north.
  • Relative velocity of A to B is at .
Step 1: Resolve the relative velocity.
  • The components of the relative velocity:
Step 2: Calculate the velocity of B.
Magnitude:
Direction:
[
\tan(\phi) =

Revisado y aprobado por el equipo de tutoría de UpStudy

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Mind Expander

Let’s dive into the world of relative motion! When car A is zipping north and car B is cruising at an angle, we can break down their speeds and angles using vector components. By calculating the differences in their velocities, we can determine how fast one car appears to be moving to the other—it’s all about perspective! Imagine a dance on the road, where each vehicle has its own rhythm!
Now, when it comes to relative velocities, keep in mind that it’s crucial to resolve the speeds into their north-south and east-west components. This can be tricky! A common mistake is forgetting the angle conversions or assuming directions without breaking down the vectors properly. So, get your calculators ready, draw a diagram, and always visualize these velocities on a grid. It makes a huge difference!

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