A stone is short-cut from a catapult with an initial velocity of 20m/s atan elevation of 40.calculate the velocity of nove height
nove height?
To calculate the final velocity at a new height, we need to consider the conservation of mechanical energy. The initial kinetic energy (KEi) of the stone will be equal to the final potential energy (PEf) at the new height. Let's go step by step to calculate the final velocity.
Step 1: Find the initial potential energy (PEi) of the stone at the initial height.
The potential energy is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximated as 9.8 m/s² at the Earth's surface), and h is the height.
Given that the stone is launched at an elevation of 40 meters, we can calculate the initial potential energy as follows:
PEi = m * g * h
= m * 9.8 * 40
Step 2: Find the initial kinetic energy (KEi) of the stone.
The kinetic energy is given by the equation KE = 0.5 * m * v², where m is the mass of the object and v is the velocity.
Given that the initial velocity of the stone is 20 m/s, we can calculate the initial kinetic energy as follows:
KEi = 0.5 * m * v²
= 0.5 * m * (20)²
Step 3: Equate the initial kinetic energy and the final potential energy.
Since the total mechanical energy remains constant, we can set the initial kinetic energy equal to the final potential energy:
KEi = PEf
0.5 * m * (20)² = m * 9.8 * h
Step 4: Cancel out the mass (m) and solve for the final velocity (vf) at the new height.
0.5 * (20)² = 9.8 * h
200 = 9.8 * h
h = 200 / 9.8
Now that we have found the new height (h), we can substitute it back into the equation above to solve for the final velocity (vf):
vf = sqrt(2 * g * h)
= sqrt(2 * 9.8 * h)
Substituting the value of h, we can calculate the final velocity (vf) at the new height.