Final answer:
In physics, potential energy and velocity calculations can be done using formulas. The potential energy of a falling object can be calculated using the mass, gravity, and height. The velocity of an object can be found using the equation involving gravity and height. The height that a bullet will reach can be determined using the Principle of Conservation of Mechanical Energy.
Step-by-step explanation:
a) The potential energy of the ball when it has fallen 3 m can be calculated using the formula: potential energy = mass * gravity * height. Assuming the mass of the ball is known, we can plug in the values to find the potential energy.
b) The velocity of the ball when it hits the ground can be determined using the equation: velocity = square root of (2 * gravity * height). Again, assuming the height is known, we can substitute the values to find the velocity.
2. a) The gravitational potential energy of the ball when it is at the top of the hill can be calculated using the formula: potential energy = mass * gravity * height.
b) The velocity of the ball when it reaches the bottom of the hill can be found using the equation: velocity = square root of (2 * gravity * height). Ignoring friction, the mass and height are given, so we can plug in these values to find the velocity.
3. The height that the bullet will reach can be determined using the Principle of Conservation of Mechanical Energy. The initial kinetic energy of the bullet is equal to the potential energy at its maximum height. We can equate these two energies and solve for the height.