Speed of the ball down the hill

Question

Ball rolls from a height of 10 metres down a slope 20metres at an angle of 30degrees. What speed does it attain?

Answer 1

I doubt it is as complicated as the previous answerer speculated:

If it isn't then u solve it using te following:

potential energy = kinetic energy

mgh = 0.5 * m * v (squared

10 * 10 = 0.5 * v (squared)

sqrt 50 m/s = v

OR u can solve this question using equations of motion where u utilize the 30 degrees and 20 metres... all depends on the level of physics ur taking.

Answer 2

You need to equate the gravitational potential energy of its height at the top minus the height at the bottom (20m*sin30) to the kinetic energy of the center of mass 1/2 mv^2 plus the rotational kinetic energy 1/2 I omega^2.  You will have to express the moment of inertia of the ball in terms of its radius squared, and write omega in terms of its speed and radius, then solve for the speed.

It might appear that need the radius of the ball, but that will miraculously drop out.

EDIT: Despite what the second answerer says, you must take the rotational motion into account.  If it said that the ball slid down the hill (rather than rolled) you would not have to.

Answer 3

use the conservation of energy here.

At the top,

when the ball is not in motion,only the potential energy would be taken into account and PE= mgh

At the bottom,

There would be 2 different energies,namely the kinetic energy and the rotational energy

As energy is conserved ,energy at the top==energy at the bottom,solve the equation.

mgh== 1/2mv^2 + 1/2Iw^2

but,v=rw or w=v/r

thus,

mgh=1/2mv^2 + 1/2mr^2 * v^2/r^2

just put in the values now..