Suppose that Vrg is the velocity of the rain drop that appears to the female observer.

All of the vectors are drawn with reference to the frame from the ground up, save for one.

Let’s say the rain is falling at the following rate:

**Case I**

A girl’s velocity is equal to Vg in the context of the problem

Suppose that Vrg is the velocity of rain in relation to the girl.

The following is the equation that is used to determine a:

${v}_{r}\u2013{v}_{g}=(a\hat{i}+b\hat{j})\u20135\hat{i}=(a\u20135)\hat{i}+b\hat{j}$Therefore,

**Case II**

The girl’s velocity has increased as a result of this = vg

The following is the equation that is used to determine the value of b at 45o tan. It can be found here.

${v}_{r}\u2013{v}_{g}=(a\hat{i}+b\hat{j})\u201310\hat{i}=(a\u201310)\hat{i}+b\hat{j}$Therefore, the velocity of rain is:

${v}_{r}=5\hat{i}\u20135\hat{j}$Speed of rain is:

$\left|{v}_{r}\right|=\sqrt{{5}^{2}+(\u20135{)}^{2}}=\sqrt{50}=5\sqrt{2}m/s$