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

Aproton is projected toward a fixed nucleus of charge +ze with velocity vo. initially the two particles are very far apart. when the proton is a distance r from the nucleus its velocity has decreased to 1/2vo. how far from the nucleus will the proton be when its velocity has dropped to 1/4vo?

Afigure skater is rotating at a rate of 200 revolutions per minute. what is the angular speed, in units of rad/s? 20.9 12000 200 3.33

Aperson stands on a platform, initially at rest, that can rotate freely without friction. the moment of inertia of the person plus the platform is ip. the person holds a spinning bicycle wheel with its axis horizontal. the wheel has moment of inertia iw and angular velocity ωw. take the ωw direction counterclockwise when viewed from above. part a what will be the angular velocity ωp of the platform if the person moves the axis of the wheel so that it points vertically upward?