Speed of ball down a hill.

Question

200gram ball rolls down a slope of 20metres at 30degree angle from a height of 10 metres. What speed does it reach? Also does it make a difference what weight the ball is? I don't think it does but curious to find out.

Acceleration ue to mass is 9.8m/s^2.

Answer 1

Use the law of conservation of energy to solve this problem.

Potential energy = Kinetic energy

PE = mgh

KE = (1/2)mV^2

where

m = mass of the body

g = acceleration due to gravity = 9.8 m/sec^2

h = initial vertical height of body's position = 10

V = velocity of body at bottom of slope

Since PE =KE,

mgh = (1/2)mV^2

and since "m" appears in both sides of the equation, it will simply cancel out, hence

gh = (1/2)V^2

and solving for "V",

V = sqrt (2gh)

Substituting appropriate values,

V = sqrt (2*9.8*10) = sqrt (196)

V = 14 m/sec.

NOTE -- in the above derivation, it was pointed out that since "m" appears in both sides of the equation, it simply cancelled each other out. Therefore, the mass of the ball is not a factor to consider in these types of problems.