Question

A ball with an initial velocity of 8.00 m/s rolls up a hill without slipping. treating the ball as a spherical shell, calculate the vertical height it reaches.

Answer 1

Answer : Height, h = 3.26 m

Explanation :

It is given that,

The ball is rolling up with an initial velocity (u) of 8 m/s.

Final velocity (v) is 0

We have to find the distance (s) or height it reaches. Using third equation of motion :

`v^2-u^2=2as`

`0-(8\ m/s)^2=2* -9.8\ m/s^2* s` (g is negative because the ball is going up)

`s=3.26\ m`

So, the vertical height reaches by the ball is 3.26 m.

Answer 2

Since we are not given with the angle of inclination of the side of the hill, it is better if it is assume here that the hill is vertically straight. Given the initial speed, the distance can be calculate through the equation,

2gd = Vf² - Vo²

Substituting the known values and keeping in mind that Vf should be 0 at the topmost of the hill,
2(-9.8 m/s²)(d) = 0 - (8 m/s)²
The value of d from the equation above is 3.265 m.