A motorist A leaves a small town and drives East at 28 ms-1 . A second motorist B is driving South towards the same town at 23 ms-1 . Draw a diagram and find the velocity of motorist B relative to motorist A? ( VB REL A )
is this just phythagoras and finding the resultant vector which is 36.24 or is it done differently.
Watch this youtube video! "Relative Velocity Lesson 3 - Example 2"
To find the velocity of motorist B relative to motorist A (VB REL A), you are correct that you can use the Pythagorean theorem to calculate the resultant vector. Here's how you can do it step by step:
1. Start by drawing a diagram to visualize the situation. Draw two axes, one representing the east-west direction and the other representing the north-south direction. Mark the starting point of both motorists.
2. Motorist A is driving east at 28 m/s. Represent this velocity on the diagram by drawing an arrow pointing to the right with a length of 28 units.
3. Motorist B is driving south towards the same town at 23 m/s. Represent this velocity on the diagram by drawing an arrow pointing downwards with a length of 23 units.
4. Now, we need to find the resultant vector, which represents the velocity of motorist B relative to motorist A (VB REL A). To do this, connect the tail of the arrow representing motorist A's velocity to the head of the arrow representing motorist B's velocity.
5. Measure the length of the resultant vector using a ruler or scale. In this case, the length is approximately 36.24 units (after rounding to two decimal places).
So, the velocity of motorist B relative to motorist A (VB REL A) is approximately 36.24 m/s.
This can also be calculated using the Pythagorean theorem:
VB REL A = sqrt(VA^2 + VB^2)
= sqrt(28^2 + 23^2)
= sqrt(784 + 529)
= sqrt(1313)
≈ 36.24 m/s
Therefore, both the Pythagorean theorem method and the diagram approach will give you the same result, approximately 36.24 m/s.