Question

If r=BT^2 I + ct^3 j, where b and c are positive constants. When does the position vector make an angle 45 with x and y axes

Answer 1

Answer:
`t=(b)/(c)`

Step-by-step explanation:

Given

The position vector is
`\vec{r}=bt^2\hat{i}+ct^3\hat{j}\\`

So, the angle made by position vector is
`45^(\circ)` at

`\Rightarrow \tan 45^(\circ)=(r_y)/(r_x)\\\\\Rightarrow \tan 45^(\circ)=(ct^3)/(bt^2)\\\\\Rightarrow bt^2=ct^3\\\\\Rightarrow t=(b)/(c)`

At
`t=(b)/(c)`, position vector makes
`45^(\circ)` with x and y axes