A race track curve has a radius of 100 m and is banked at an angle of 68∘. For what speed was the curve designed, neglecting friction? Solve using first principles, not just a single memorized equation for full marks.
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A race track curve has a radius of and is banked at an angle of . For what speed was the curve designed, neglecting friction? Solve using first principles, not just a single memorized equation for full marks.
![A 50 kg child stands on the edge of a stationary thin rod of length 5.0 m and mass M = 100 kg, free to rotate around its center of mass O. The child catches a ball of mass 2.0 kg thrown by a friend. Just before the ball is caught, the ball has a horizontal velocity of magnitude 30 ms−1, at angle θ = π/4 with a rod, as shown in Fig. 4 (a) What is the angular speed of the thin rod just after the ball is caught? (b) What is the mechanical energy of the child after the ball has been caught? [6 marks] (c) With what horizontal velocity, at an angle ϕ = π/6 with respect to the rod, has the boy to throw away the ball such that after the launch he will stay at rest? [7 marks]](https://www.doubtrix.com/uploads/editor/9895436237ysrDMhQJnq.png)