A body with a mass of 75 kg is located at a height of 20 m. If it is allowed to free fall to the ground. What will be its velocity on impact?
KEfinal=PEinitial-frictionlosses
1/2 m v^2=mgh-0
solve for v
1/2* 75kg* v^2= 75kg* 9.81* 20-0
37.5* v^2= 14715
37.5* v^2/ 37.5= 14715/37.5
v^2= 14715/37.5
v^2= 392.4 m/s
a body with a mass of 75 kg is located at a height of 20 m.If it is allowed to fall freely to the ground.What will be its velocity on impact?
To find the velocity of the body on impact, we can apply the laws of motion and the principles of free fall.
1. Start by determining the initial gravitational potential energy of the body. The formula for gravitational potential energy is:
Potential Energy = mass * gravitational acceleration * height
The mass of the body is given as 75 kg, the gravitational acceleration is approximately 9.8 m/s², and the height is 20 m. So, the potential energy is:
Potential Energy = 75 kg * 9.8 m/s² * 20 m
2. Next, we need to find the final kinetic energy of the body just before it impacts the ground. According to the law of conservation of energy, the potential energy at the top is converted into kinetic energy at the bottom.
Kinetic Energy = Potential Energy
Therefore, the kinetic energy is also equal to:
Kinetic Energy = 75 kg * 9.8 m/s² * 20 m
3. Now, we can calculate the velocity using the formula for kinetic energy:
Kinetic Energy = 1/2 * mass * velocity²
Rearranging the formula, we get:
velocity² = (2 * Kinetic Energy) / mass
4. Plugging in the values, we have:
velocity² = (2 * (75 kg * 9.8 m/s² * 20 m)) / 75 kg
Simplifying,
velocity² = 2 * 9.8 m/s² * 20 m
velocity² = 2 * 196 m²/s²
velocity² = 392 m²/s²
5. Finally, taking the square root of both sides, we find:
velocity = √(392 m²/s²)
velocity ≈ 19.8 m/s
Therefore, the velocity of the body on impact will be approximately 19.8 m/s.