A gun converts 200J of stored energy into kinetic energy of the 0.02kg bullet. What is the speed of the bullet as it leaves the gun? If the gun is fired straight up how high will the bullet go?

a. KE = 0.5*M*Vo^2

KE = 200 J.
M = 0.02 kg
Solve for Vo, the initial velocity.

b. M*g*h = 200
M = 0.02 kg
9 = 9.8 m/s^2
Solve for h.

To find the speed of the bullet as it leaves the gun, we can use the principle of conservation of energy. The total energy of the bullet consists of its initial potential energy (stored energy in the gun) and its final kinetic energy.

The initial potential energy is given as 200J, and we know that this energy is converted into kinetic energy. Therefore, the final kinetic energy is also 200J.

The kinetic energy of an object can be calculated using the equation:

KE = 1/2 * m * v^2

Where:
KE is the kinetic energy,
m is the mass of the object, and
v is the velocity (speed) of the object.

In this case, the mass of the bullet is given as 0.02kg. Substituting the values into the equation, we can solve for the speed of the bullet:

200J = 1/2 * 0.02kg * v^2

Dividing both sides of the equation by 1/2 * 0.02kg, we get:

v^2 = 200J / (1/2 * 0.02kg)

v^2 = 200J / 0.01kg

v^2 = 20,000m^2/s^2

Taking the square root of both sides of the equation, we find:

v ≈ √(20,000m^2/s^2)

v ≈ 141.42 m/s

Therefore, the speed of the bullet as it leaves the gun is approximately 141.42 m/s.

Now, let's move on to the second part of the question: If the gun is fired straight up, how high will the bullet go?

To determine the maximum height the bullet reaches when fired straight up, we can use the principles of projectile motion and apply the kinematic equations. In this case, the only force acting on the bullet is gravity.

The maximum height can be calculated using the equation:

h = (v^2) / (2g)

Where:
h is the maximum height,
v is the initial vertical velocity (which is equal to the speed of the bullet in this case), and
g is the acceleration due to gravity (approximately 9.8m/s^2 on Earth).

Substituting the value of v from the previous calculation, we have:

h = (141.42 m/s)^2 / (2 * 9.8 m/s^2)

h ≈ 1010.20 m

Therefore, when fired straight up, the bullet will reach a maximum height of approximately 1010.20 meters.