When will the velocity vector make an angle of 45 degrees?

[bharp24]

i have been given that vector r = bt^2i + ct^3j where b and c are positive constants, and i need to know when the velocity vector will make an angle of 45 degrees.

i have been trying to figure it out and am just confused. i have taken the derivative of vec r, because i know that it becomes velocity but i don't know what to do from there. i cannot figure out the components of what makes up the velocity vector. i feel like i am going in circles. please someone help!

 

[Doc Al]

Hint: When the velocity vector makes an angle of 45 degrees with respect to the horizontal, what can you say about $V_y/V_x$?

 

[bharp24]

it will = 1 because the sin and cos of 45 degrees are the same...right?

 

[Doc Al]

Right!