Question

How do I solve this problem?

Answer 1

To solve this question we will compute the magnitude of each vector.

Recall that the magnitude of a vector

`a\hat{i}+b\hat{j}`

is:

`\parallel a\hat{i}+b\hat{j}\parallel=\sqrt[]{a^2+b^2}.`

Therefore, the speed of the first car is:

`\parallel26\hat{i}+31\hat{j}\parallel=\sqrt[]{26^2+31^2}\text{.}`

Simplifying the above equation we get:

`\parallel26\hat{i}+31\hat{j}\parallel=\sqrt[]{676^{}+961}=\sqrt[]{1637}\approx40.46.`

The speed of the second car is:

`\parallel40\hat{i}\parallel=\parallel40\hat{i}+0\hat{j}\parallel=\sqrt[]{40^2+0^2}\text{.}`

Simplifying the above equation we get:

`\parallel40\hat{i}\parallel=\sqrt[]{40^2}=40\text{.}`

Answer:

The first car is the faster car.

Speed= 40.46.