quick m2 question

The impulse is in the direction of i-j, so I = C(i-j) for some constant C. You're told that the magnitude of the impulse is

9\sqrt{2}

, and so

|C(\mathbf{i}-\mathbf{j})| = 9\sqrt{2}

, and so

C=\cdots

[you do this bit].

The impulse is in the direction of i-j, so I = C(i-j) for some constant C. You're told that the magnitude of the impulse is

9\sqrt{2}

, and so

|C(\mathbf{i}-\mathbf{j})| = 9\sqrt{2}

, and so

C=\cdots

[you do this bit].

so its just guess work at what i and j components could be? surely there are several possibilities?

Original post by jumblebumble

so its just guess work at what i and j components could be? surely there are several possibilities?

There's no guesswork at all. A vector is defined by its direction and magnitude. It says that the impulse is in the same direction as

\mathbf{i}-\mathbf{j}

and has magnitude

9\sqrt{2}

, so you can work out what the vector is. Saying "it's in the same direction as

\mathbf{i}-\mathbf{j}

" means "it's a (positive) scalar multiple of

\mathbf{i}-\mathbf{j}

"; in other words,

\mathbf{I} = C(\mathbf{i}-\mathbf{j})

for some positive number

C

. The magnitude then determines the value of

C

, which you can find by taking the length of

C(\mathbf{i}-\mathbf{j})

in terms of

C

, and then solving for

C

.

If it helps, write

\begin{pmatrix} 1 \\ -1 \end{pmatrix}

instead of

\mathbf{i}-\mathbf{j}

. They mean the same thing.

(edited 13 years ago)

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