Sam stands on a 20 m high cliff and throws a 45 g rock with an initial velocity of 5 m/s [forward] to the water below. Use the conservation of energy to determine the speed of the rock when it has fallen 12 m.

v = 12.52 [m/s]

Explanation:

To solve this problem we must use the energy conservation theorem. Which tells us that potential energy is transformed into kinetic energy or vice versa. This is more clearly as the potential energy decreases the kinetic energy increases.

Ep = Ek

where:

Ep = potential energy [J] (units of joules]

Ek = kinetic energy [J]

Ep = m*g*h

where:

m = mass of the rock = 45 [g] = 0.045 [kg]

g = gravity acceleration = 9.81 [m/s²]

h = elevation = (20 - 12) = 8 [m]

Ek = 0.5*m*v²

where:

v = velocity [m/s]

The reference level of potential energy is taken as the ground level, at this level the potential energy is zero, i.e. all potential energy has been transformed into kinetic energy. In such a way that when the Rock has fallen 12 [m] it is located 8 [m] from the ground level.

m*g*h = 0.5*m*v²

v² = (g*h)/0.5

v = √(9.81*8)/0.5

v = 12.52 [m/s]

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s

b. lifting dumbbell weight at 20-degree angle from the body after a 45-degree angle