We can use the conservation of momentum to solve. Since the satellites stick together, there is only one final velocity term.

We know the masses for both satellites are equal, and the second satellite is initially stationary.

Now we need to find the velocity of the first satellite. Since the satellite is in orbit (circular motion), we need to find the tangential velocity. We can do this by finding the centripetal acceleration from the centripetal force.

Recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .

Solve for for the satellite. To do this, use the law of universal gravitation.

Remember that r is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleration. Remember that centripetal force is Fc=m∗ac. Set our two forces equal and solve for the centripetal acceleration.

Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!

This value is the tangential velocity, or the initial velocity of the first satellite. We can plug this into the equation for conversation of momentum to solve for the final velocity of the two satellites.

We can use the conservation of momentum to solve. Since the satellites stick together, there is only one final velocity term.

We know the masses for both satellites are equal, and the second satellite is initially stationary.

Now we need to find the velocity of the first satellite. Since the satellite is in orbit (circular motion), we need to find the tangential velocity. We can do this by finding the centripetal acceleration from the centripetal force.

Recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .

Solve for for the satellite. To do this, use the law of universal gravitation.

Remember that r is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleration. Remember that centripetal force is Fc=m∗ac. Set our two forces equal and solve for the centripetal acceleration.

Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!

This value is the tangential velocity, or the initial velocity of the first satellite. We can plug this into the equation for conversation of momentum to solve for the final velocity of the two satellites.

To solve this problem we need to divide up the situation into two parts. During the first part the person is jumping from the roof of a house and is therefore undergoing freefall and accelerated motion due to the force of gravity. Therefore we will need to use kinematic equations to solve for the final velocity as the person lands. In the second part of the problem, the person decelerates their torso through a specific distance and comes to a stop. We will then need to calculate the acceleration of the torso during this second part to determine the average force applied.

Let us start with kinematics to determine the speed of the torso as it hits the ground.

Knowns

We can use the kinematic equation

This is the velocity of the torso as it hits the ground. We will know use the same equation with new variables to determine the acceleration of the torso as it comes to a stop.

Knowns

Rearrange to get the acceleration by itself

We can now plug this into Newton’s 2nd Law to find the average force acting on the object.

For this problem, we'll use Newton's third law, which states that for every force there will be another force equal in magnitude, but opposite in direction.

This means that the force of the first skater on the second will be equal in magnitude, but opposite in direction:

Use Newton's second law to expand this equation.

We are given the mass of each skater and the acceleration of the first. Using these values, we can solve for the acceleration of the second.

From here, we need to isolate the acceleration of the second skater.

Notice that the acceleration of the second skater is negative. Since she is moving in the opposite direction of the first skater, one acceleration will be positive while the other will be negative as acceleration is a vector.

For this problem, we'll use Newton's third law, which states that for every force there will be another force equal in magnitude, but opposite in direction.

This means that the force of the first skater on the second will be equal in magnitude, but opposite in direction:

Use Newton's second law to expand this equation.

We are given the mass of each skater and the acceleration of the first. Using these values, we can solve for the acceleration of the second.

From here, we need to isolate the acceleration of the second skater.

Notice that the acceleration of the second skater is negative. Since she is moving in the opposite direction of the first skater, one acceleration will be positive while the other will be negative as acceleration is a vector.

To solve this problem we need to divide up the situation into two parts. During the first part the person is jumping from the roof of a house and is therefore undergoing freefall and accelerated motion due to the force of gravity. Therefore we will need to use kinematic equations to solve for the final velocity as the person lands. In the second part of the problem, the person decelerates their torso through a specific distance and comes to a stop. We will then need to calculate the acceleration of the torso during this second part to determine the average force applied.

Let us start with kinematics to determine the speed of the torso as it hits the ground.

Knowns

We can use the kinematic equation

This is the velocity of the torso as it hits the ground. We will know use the same equation with new variables to determine the acceleration of the torso as it comes to a stop.

Knowns

Rearrange to get the acceleration by itself

We can now plug this into Newton’s 2nd Law to find the average force acting on the object.

Newton's third law states that when one object exerts a force on another object, that second object exerts a force of equal magnitude, but opposite in direction on the first.

That means that:

Using the value from the question, we can find the force of the ground on the boy.

For this problem, we'll use Newton's third law, which states that for every force there will be another force equal in magnitude, but opposite in direction.

This means that the force of the first skater on the second will be equal in magnitude, but opposite in direction:

Use Newton's second law to expand this equation.

We are given the acceleration of each skater and the mass of the first. Using these values, we can solve for the mass of the second.

Notice that the acceleration of the second skater is negative. Since she is moving in the opposite direction of the first skater, one acceleration will be positive while the other will be negative as acceleration is a vector. From here, we need to isolate the mass of the second skater.

When you are slowing down the car, the fuzzy dice want to keep moving forward. Therefore the angle they make will be toward the windshield. The force of tension on the fuzzy dice is what is holding them back with the car, keeping them from going through the windshield. This tension force is comprised of two components. The y-component of the tension is equal to the force of gravity acting on the fuzzy dice. The x-component of the tension is equal to the force of the car slowing down.

The angle of the fuzzy dice is related to these two components through the trigonometric function tangent.

We can then use in the inverse tan function to determine the angle acting on the fuzzy dice.

Notice how the mass of the dice falls out of the equation

We can now plug in our values and solve.

For this problem, we'll use Newton's third law, which states that for every force there will be another force equal in magnitude, but opposite in direction.

This means that the force of the first skater on the second will be equal in magnitude, but opposite in direction:

Use Newton's second law to expand this equation.

We are given the acceleration of each skater and the mass of the first. Using these values, we can solve for the mass of the second.

Notice that the acceleration of the second skater is negative. Since she is moving in the opposite direction of the first skater, one acceleration will be positive while the other will be negative as acceleration is a vector. From here, we need to isolate the mass of the second skater.