Vector help !?

Question

Please help me with these 2 questions:
Calculate the resultant velocity (diagonal) of a pair of 100 km/h velocities at right angles to each other

If a 14-unit vector make an angle of 45 degrees with the horizontal, what are its horizontal and vertical components ?

Answer 1

OK missy -

I can do this without my calculator, which is downstairs anyway.

Two vectors - one goes straight with a length of 100 and then the next one starts from there and turns right (say) and goes out there for a length of 100. So if we connect the starting point to the ending point, we have the resultant. This will be a diagonal off to the right from the tail of the first vector to the head of the second one. Since both vectors are equal in length and form a right angle, then if we look down on this situation we will see a right triangle with one right angle and two 45 degree angles. Have you taken trig? I hope so. The length of the hypotenuse is 100/ sin (45 deg) = 141.4

So that's the magnitude of the resultant vector. It's direction is in the diagonal from start to finish as described above.

The second half of the problem just works the same problem in reverse. With a 45 degree angle to the horizontal, it must also make a 45 degree angle to the vertical, and we have the same kind of triangle, but with shorter sides. With a hypotenuse of 14. the sides must be pretty close to 10 on each side (vertical and horizontal).

Hope this helps.

Answer 2

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Answer 3

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