Question

A ball has an initial velocity of 3 m/s. If there is no friction, what is the highest it could roll?

Answer 1

Here we can use energy conservation because there is no friction in this setup

now we can say

$KE_i + PE_i = KE_f + PE_f$

here we will have

$v_i = 3 m/s$

$PE_i = 0$

at the maximum height position its speed will become ZERO

So we can say

$KE_f = 0$

now from above equation

$\frac{1}{2}m(3)^2 + 0 = m(9.81)(h) + 0$

now we have

$4.5 = 9.81 h$

$h = 0.46 m$