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]

d) physical means can be used to separate the components of air.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west