On planet Tehar, the free fall acceleration is the same as that on the Earth, but there is also a strong downward electric field that is uniform close to the planets surface. A 2.00k ball having a charge of 5.00C is thrown upward at a speed of 20.1 m/s. It hits the ground after an interval of 4.10s. What is the acceleration of a freely falling object on Tehar

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To find the acceleration of a freely falling object on planet Tehar, we need to consider the balance between the gravitational force and the electric force.

The acceleration due to gravity on planet Tehar is the same as on Earth, which is approximately 9.8 m/s^2.

However, on planet Tehar, there is also a strong downward electric field. This electric field will exert an electric force on any charged object in its vicinity. In this case, the charged object is the ball with a charge of 5.00C.

To find the electric force, we can use the equation:

Electric force = Charge * Electric field

Given that the charge of the ball is 5.00C and the electric field is uniform and close to the planet's surface, we can assume that the electric field remains constant.

Next, we need to determine the direction of the electric force. Since the ball has a positive charge, and the electric field is strong and downward, the electric force will act in the opposite direction of the electric field. So, it will be upwards.

Now, let's consider the motion of the ball. It is thrown upward with an initial velocity of 20.1 m/s. It then goes against the gravitational force and the electric force. The ball eventually hits the ground after a time interval of 4.10s.

The key here is that the ball eventually hits the ground. This means that the net force acting on the ball (the vector sum of all the forces) must be downward, causing the acceleration to be positive and in the downward direction.

Since the acceleration due to gravity is always directed downward and has a magnitude of 9.8 m/s^2, we can conclude that the magnitude of the electric force (upward) must be greater than the magnitude of the gravitational force (downward) to slow down and eventually stop the ball, causing it to fall back to the ground.

So, the net force acting on the ball is the sum of the gravitational force and the electric force, and it must be greater than zero. Mathematically, we can write it as:

Net force = Gravitational force + Electric force > 0

Applying Newton's second law of motion, we know that the net force equals the mass of the ball multiplied by its acceleration. Therefore, we have:

Mass of the ball * Acceleration = Gravitational force + Electric force > 0

Given that the mass of the ball is 2.00 kg, we can rearrange the equation to solve for the acceleration:

Acceleration = (Gravitational force + Electric force) / Mass of the ball

Now, we need to calculate the gravitational force and the electric force:

Gravitational force = Mass of the ball * Acceleration due to gravity

Electric force = Charge of the ball * Electric field

With these values, we can now substitute them back into the equation to find the acceleration:

Acceleration = (Mass of the ball * Acceleration due to gravity + Charge of the ball * Electric field) / Mass of the ball

Plugging in the known values, we have:

Acceleration = (2.00 kg * 9.8 m/s^2 + 5.00 C * Electric field) / 2.00 kg

Since the acceleration is not explicitly given in the question, we cannot calculate the exact value without knowing the electric field on planet Tehar. To find the value of the acceleration, we would need to know the magnitude and direction of the electric field.