Adding and Subtracting vectors; Finding change in velocity

In summary, the cricketer is facing north and square leg is west of him. The change in velocity of the cricket ball is 58m/s N59°W, which is the same as W31°N. This can be determined by using the equation Δv= Final velocity subtract initial velocity and taking the inverse tangent of the opposite over adjacent sides. However, using the adjacent over opposite sides will also give the same direction.
  • #1
ShannonBanana
2
0

Homework Statement



A batsman hits a cricket ball traveling towards him at 30m/s over square leg at 50m/s. If the cricketer is facing north and square leg is west of him, what is the change in velocity of the ball?

Homework Equations



Δv= Final velocity subtract initial velocity.

The Attempt at a Solution



I've attached a picture of my working, so you might be able to see where I've gone wrong. From this diagram, I got correct the final "speed" but not the direction. My answer was Δv=58m/s N59°W, but the answer given says the direction should be W31°N.
I got my answer through tan-1(50/30) or tan-1(opposite over adjacent). To get the answer given, you would have to (by my reckoning) use adjacent over opposite, which doesn't seem to be right. Do I have θ in the right place? And, if so, why?

Thanks for the help :)
 
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  • #2
ShannonBanana said:
N59°W, but the answer given says the direction should be W31°N.
Aren't they the same?
 
  • #3
... Are you serious?? Wow, I'm feeling kind of dumb now... Thank you though! :D
 

FAQ: Adding and Subtracting vectors; Finding change in velocity

1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is typically represented by an arrow, with the length of the arrow indicating the magnitude and the direction of the arrow indicating the direction.

2. How do you add vectors?

To add vectors, you must first ensure that they are in the same coordinate system. Then, add the corresponding components of each vector (e.g. x-component of vector 1 + x-component of vector 2) to find the x-component of the resulting vector. Repeat this process for the y-component and z-component (if applicable) to find the complete resulting vector.

3. What is the difference between adding and subtracting vectors?

Adding vectors combines their magnitudes and directions, while subtracting vectors involves finding the difference between their magnitudes and directions. In other words, adding vectors results in a larger vector, while subtracting vectors results in a smaller vector or a vector in the opposite direction.

4. How do you find the change in velocity using vectors?

The change in velocity can be found by subtracting the initial velocity vector from the final velocity vector. This will result in a vector representing the change in velocity, with its magnitude indicating the amount of change and its direction indicating the direction of the change.

5. Can you add vectors in any order?

Yes, the order in which you add vectors does not affect the result. This is known as the commutative property of vector addition. However, it is important to ensure that all vectors are in the same coordinate system before adding them.

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