Could you please explain to me these problems, I don't understand them.

Do 100 J of work in 50 s and your power output is?

A bow is drawn so that it has 40 J of potential energy. When fired, the arrow will ideally have a kinetic energy of ?

A diver who weighs 500 N steps off a diving board that is 10 m above the water. The diver hits the water with kinetic energy of?

Sure! I'll explain how to solve each problem step by step.

Problem 1: Work and Power
To find the power output, we first need to understand the relationship between work and power. Power is defined as the rate at which work is done. It can be calculated using the equation:

Power = Work/Time

In this case, we are given that 100 Joules (J) of work is done in 50 seconds (s). So, we can substitute these values into the equation:

Power = 100 J / 50 s

Calculating this, we find that the power output is 2 Joules per second, or 2 Watts.

Problem 2: Potential and Kinetic Energy
In this problem, we need to find the kinetic energy of an arrow when it is fired, given its potential energy. To do this, we need to understand the relationship between potential energy and kinetic energy. The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another.

The potential energy (PE) of an object is given by the equation:

PE = m * g * h

where m is the mass, g is the acceleration due to gravity, and h is the height. The kinetic energy (KE) of an object is given by the equation:

KE = 1/2 * m * v^2

where v is the velocity of the object.

In this case, we are given that the potential energy of the bow is 40 J. However, it's important to note that potential energy is not equal to kinetic energy. When the arrow is fired, some of the potential energy will be converted to kinetic energy, while some may be lost due to other factors like air resistance.

Therefore, it's not possible to determine the exact kinetic energy of the arrow without additional information, such as the mass of the arrow or its velocity when fired.

Problem 3: Kinetic Energy of a Diver
To find the kinetic energy of the diver when hitting the water, we again need to understand the relationship between kinetic energy and other variables. The kinetic energy (KE) is given by the equation:

KE = 1/2 * m * v^2

where m is the mass of the object and v is the velocity.

In this case, we are given that the diver weighs 500 Newtons (N) and is diving from a height of 10 meters (m) above the water. However, the weight of an object (measured in Newtons) is not the same as its mass (measured in kilograms). To find the mass, we need to divide the weight by the acceleration due to gravity (9.8 m/s^2).

So, the mass (m) of the diver can be calculated as:

m = 500 N / 9.8 m/s^2

Once you find the mass, you can substitute it into the kinetic energy equation along with other known values to calculate the kinetic energy of the diver when hitting the water.