a rock is thrown at a downwards angle of 15 degrees from the top of a 120 m cliff with a speed of 25 m/s. what will be its speed when it strokes the ground at the base of the cliff?
I know to use the conservation of energy but I don't know how to set it up.
To solve this question using the conservation of energy, we can consider the initial energy of the rock at the top of the cliff and its final energy when it hits the ground. By assuming no energy is lost due to air resistance, we can equate the two energy states and find the final speed of the rock.
Let's break down the problem step by step:
Step 1: Calculate the initial potential energy (PEi) of the rock at the top of the cliff.
- The formula for potential energy is PE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height.
- In this case, the mass of the rock is not given, but we can assume it cancels out on both sides of the equation.
- The initial potential energy (PEi) at the top of the cliff will be equal to m * g * h.
Step 2: Calculate the initial kinetic energy (KEi) of the rock at the top of the cliff.
- The formula for kinetic energy is KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
- In this case, the mass of the rock is not given, but we can assume it cancels out on both sides of the equation.
- The initial kinetic energy (KEi) at the top of the cliff will be equal to (1/2) * m * v^2.
Step 3: Calculate the final potential energy (PEf) of the rock at the base of the cliff.
- Since the rock is at the base of the cliff, its height (h) will be zero.
- Therefore, the final potential energy (PEf) will be zero.
Step 4: Equate the initial and final energies and solve for the final kinetic energy (KEf).
- PEi + KEi = PEf + KEf
Step 5: Substitute the known values into the equation and solve for the final velocity (vf).
- Plug in the values you know:
- PEi = m * g * h
- KEi = (1/2) * m * v^2
- PEf = 0
- KEf = (1/2) * m * vf^2
- Simplify the equation and solve for vf.
By following these steps, you should be able to find the final velocity (vf) of the rock when it strikes the ground at the base of the cliff.