A) Calculate the kinetic energy of a 5.0g bullet travelling with a velocity of 400^ms-1.

B) Calculate the gravitational potential energy relative to the ground when a bird of mass 105g is 400m above the ground.

Learn these formulas.

kinetic energy = (1/2) M V^2
potential energy = M g H

g is the acceleration of gravity, and H is the height above ground. M and V have obvious meanings

Now, do the calculations.

For energy in joules, mass M must be in kg.

A) To calculate the kinetic energy of an object, you can use the following formula:

Kinetic Energy = 1/2 * mass * velocity^2

Given that the mass of the bullet is 5.0g (0.005kg) and the velocity is 400 m/s, we can substitute these values into the formula:

Kinetic Energy = 1/2 * 0.005kg * (400 m/s)^2

First, let's square the velocity:

Kinetic Energy = 1/2 * 0.005kg * 160000 m^2/s^2

Next, multiply the mass by the squared velocity:

Kinetic Energy = 0.5 * 0.005kg * 160000 m^2/s^2

Finally, calculate the value:

Kinetic Energy = 400 J

So, the kinetic energy of the 5.0g bullet traveling at 400 m/s is 400 Joules (J).

B) To calculate the gravitational potential energy of an object, you can use the following formula:

Gravitational Potential Energy = mass * acceleration due to gravity * height

Given that the mass of the bird is 105g (0.105kg), the acceleration due to gravity is approximately 9.81 m/s^2 (assuming we are near the surface of the Earth), and the height is 400m, we can substitute these values into the formula:

Gravitational Potential Energy = 0.105kg * 9.81 m/s^2 * 400m

Multiply the mass, acceleration due to gravity, and height together:

Gravitational Potential Energy = 0.105kg * 9.81 m/s^2 * 400m

Finally, calculate the value:

Gravitational Potential Energy = 411.84 J

So, the gravitational potential energy relative to the ground when the bird is 400m above the ground is approximately 411.84 Joules (J).