1.a ball with a mass 2kg rests on an incline with an angle of 10 degrees. The ball is released to roll down the incline plane neglecting all friction:

Determine the following:

A.the loss in potential energy after it has rolled 12m.
B. The kinetic energy
C.the velocity after it has rolled 12m.
D.the original height that the ball ,as rolled from in order to reach the bottom of the slope at 20m/s

What about if we say EP=mgh12sin10

=2*9.8*12sin10
=40,84J

But tshepo that 12m is not a Height ita a Distance

You have to calculate height first

A. The loss in potential energy can be calculated using the formula:

Loss in potential energy = mass * gravitational acceleration * height
Since the ball is resting on an incline at an angle of 10 degrees, the height can be calculated using trigonometry:
height = 12m * sin(10 degrees)
Substituting the given values:
Loss in potential energy = 2kg * 9.8 m/s^2 * 12m * sin(10 degrees)

B. The kinetic energy can be calculated using the formula:
Kinetic energy = 0.5 * mass * velocity^2
We need to calculate the velocity first in order to determine the kinetic energy.

C. To calculate the velocity, we can use the conservation of mechanical energy:
Loss in potential energy = Gain in kinetic energy
So, the loss in potential energy can be equaled to the kinetic energy. Using the formula from part A and substituting the given values, we can solve for the velocity.

D. To find the original height, we can calculate the loss in potential energy when the ball rolls down to the bottom with a velocity of 20m/s and solve for the height.

To determine the answers to the questions, we need to use the principles of conservation of energy and the laws of motion.

A. Loss in Potential Energy:
The potential energy (PE) of an object is given by the equation PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height. In this case, the potential energy is equal to the initial potential energy since the ball is initially at rest. Therefore, the loss in potential energy is zero, as there is no initial potential energy to lose.

B. Kinetic Energy:
The kinetic energy (KE) of an object is given by the equation KE = 1/2 * m * v², where m is the mass of the object and v is its velocity. When the ball reaches the bottom of the slope, its potential energy is converted into kinetic energy. So the kinetic energy at the bottom of the slope can be calculated using the mass of the ball and the height of the slope. Since there is no friction, there is no loss of energy. So the kinetic energy at the bottom of the slope is equal to the initial potential energy.

C. Velocity:
Since the ball starts from rest, we can use the principle of conservation of energy to determine the velocity after it has rolled 12m. We equate the loss in potential energy to the gain in kinetic energy:
m * g * h = 1/2 * m * v²
Simplifying the equation, we get:
v = sqrt(2 * g * h)

Plugging in the values of g (9.8 m/s²) and h (12 m), we can calculate the velocity.

D. Original Height:
To determine the original height that the ball was rolled from, we can use the equation of motion for uniformly accelerated rectilinear motion:
v² = u² + 2 * a * s
where v is the final velocity (20 m/s), u is the initial velocity (0 m/s), a is the acceleration (given by g * sin(θ), where θ is the angle of the incline), and s is the displacement (12 m).

Using this equation, we can solve for the initial height (s):

20² = 0 + 2 * g * sin(10°) * s
Simplifying the equation, we get:
s = 20² / (2 * g * sin(10°))

Plugging in the values of g (9.8 m/s²) and the angle (10°), we can calculate the initial height.

1.2.1Ep=mgh

=(2)(9,8)(12)
=235,2J

1.2.2Ep=Ek
Ek=235,2J

1.2.3 Ek=1/2mv^2
235,2 =(1/2)(2)v
(235,2)^1/2=(V^2)^1/2
15.336m/s=v

1.2.4 V^2=U^2 + 2as
20^2=0 + (2)(9.8)s
400=19,6s
400/19,6=s
20,408m=s