A right-triangular box is fixed in place in the xy plane, with its vertices at (x,y) values of (0,0), (1,0), and (0,1). A ball is initially at (0.3,0.5), with a velocity vector (v_x,v_y) of (5,−7). The ball bounces off of the sides of the box.

If x′ and y′ are the coordinates of the ball on its 1000th bounce, give your answer as ⌊1000 (x′+y′)⌋.

Details and Assumptions:

When the ball bounces off of a surface (side), the normal component of the velocity is negated and the tangential portion of the velocity is preserved.

There are no forces at play when the ball is traversing the interior of the box.

⌊⋅⌋ denotes the floor function

Question

A right-triangular box is fixed in place in the xy plane, with its vertices at (x,y) values of (0,0), (1,0), and (0,1). A ball is initially at (0.3,0.5), with a velocity vector (v_x,v_y) of (5,−7). The ball bounces off of the sides of the box.

If x′ and y′ are the coordinates of the ball on its 1000th bounce, give your answer as ⌊1000 (x′+y′)⌋.

Details and Assumptions:

When the ball bounces off of a surface (side), the normal component of the velocity is negated and the tangential portion of the velocity is preserved.

There are no forces at play when the ball is traversing the interior of the box.

⌊⋅⌋ denotes the floor function

Macho14 · Answer

the answer is 485 I am pretty sure please check

ironm4n · Answer

correct my boy