Answer to Question #265254 in Mechanics | Relativity for marie

Question

Two identical balls, A and B, are released from rest from the same height, 2.8 m, along two smooth inclined planes that touch the horizontal ground. Ball A is released on a plane inclined at 30⁰ to the horizontal. The plane on which ball B is released is inclined at 60⁰ to the horizontal. Ignore energy due to rotation of the balls. [Diagrams, but no forces]

a) What is the speed of each ball at the bottom of their respective inclined planes?

b) Which ball would reach the bottom first? Explain your answer.

Answer 1

a) The speed is the same for both balls:

$$v=\sqrt{2gh}=\sqrt{2·2.8·9.8}=7.4\text{ m/s}.$$

b) The first will be the ball released along a 60°-slope because it is more vertical, therefore, the acceleration due to gravity will influence its motion more.