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

Question

asked Feb 28, 2022 108k views

1 Answer

CAD · Answer 1 · 2022-03-05T17:31:43+0000

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