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M1 Vectors Question

I've attached the question and the mark scheme. I understand everything except part d, the thing I'm most confused about is the 8/5 - I understand where the values come from but not why they're divided.

Thanks is advance.

ImageUploadedByStudent Room1461578775.064276.jpg
ImageUploadedByStudent Room1461578799.250818.jpg



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Reply 1
Original post by meloj
I've attached the question and the mark scheme. I understand everything except part d, the thing I'm most confused about is the 8/5 - I understand where the values come from but not why they're divided.

Thanks is advance.

ImageUploadedByStudent Room1461578775.064276.jpg
ImageUploadedByStudent Room1461578799.250818.jpg



Posted from TSR Mobile

If BB moves in the direction of 3i+4j3\mathbf{i} + 4\mathbf{j} then the velocity must be of the form k(3i+4j)k(3\mathbf{i} + 4\mathbf{j})

Now the magnitude of 3i+4j3\mathbf{i} + 4\mathbf{j} is 55 but we need a magnitude of 88 so we need to multiply the vector by 85\frac{8}{5}

This works now since the magnitude of 85(3i+4j)\frac{8}{5}(3\mathbf{i} + 4\mathbf{j}) is 85×5=8\frac{8}{5}\times 5 = 8.
since the direction of B is 3i+ 4j then a unit vector of velocity in that direction would be

{1/5}{3i+ 4j}.... this means the speed would be 1 m/s.

Since we want 8 m/s you multiply by 8

=====> {8/5}{3i+ 4j}
Reply 3
Original post by notnek
If BB moves in the direction of 3i+4j3\mathbf{i} + 4\mathbf{j} then the velocity must be of the form k(3i+4j)k(3\mathbf{i} + 4\mathbf{j})

Now the magnitude of 3i+4j3\mathbf{i} + 4\mathbf{j} is 55 but we need a magnitude of 88 so we need to multiply the vector by 85\frac{8}{5}

This works now since the magnitude of 85(3i+4j)\frac{8}{5}(3\mathbf{i} + 4\mathbf{j}) is 85×5=8\frac{8}{5}\times 5 = 8.


Thanks for your help! I understand it now :smile:
Reply 4
Thanks for your help! Much appreciated :smile:

Original post by the bear
since the direction of B is 3i+ 4j then a unit vector of velocity in that direction would be

{1/5}{3i+ 4j}.... this means the speed would be 1 m/s.

Since we want 8 m/s you multiply by 8

=====> {8/5}{3i+ 4j}

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