A body of 150kg is located at a height of 45m. If allowed to fall freely to the ground. What will be its velocity on impact?
mgh= mv²/2
v=sqrt(2gh)
a 75kg person jumps from a height of 2m on to the ground
To determine the velocity of the body just before it impacts the ground, we can use the equation for gravitational potential energy (PE) and kinetic energy (KE):
PE = mgh
KE = 1/2mv^2
Where:
m = mass of the body (150 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height (45 m)
v = velocity
Initially, the body has only potential energy at height h. As it falls, this potential energy is converted into kinetic energy just before it hits the ground.
Step 1: Calculate the potential energy of the body at height h.
PE = mgh
PE = (150 kg)(9.8 m/s^2)(45 m)
PE = 66150 J
Step 2: Set the potential energy equal to the kinetic energy.
PE = KE
KE = 66150 J
Step 3: Calculate the velocity using kinetic energy equation.
KE = 1/2mv^2
66150 J = 1/2(150 kg)(v^2)
132300 J = (150 kg)(v^2)
v^2 = 132300 J / (150 kg)
v^2 = 882 m^2/s^2
Step 4: Take the square root of both sides to find the velocity.
v = √(882 m^2/s^2)
v ≈ 29.7 m/s
Therefore, the velocity of the body just before it impacts the ground will be approximately 29.7 m/s.
To find the velocity of the body on impact, we can use the principle of conservation of energy. At a certain height h, the body has potential energy (PE) which can be converted into kinetic energy (KE) when it reaches the ground.
The potential energy of an object is given by the equation PE = mgh, where m is the mass of the object (150 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height (45 m).
So, the potential energy (PE) of the body at height 45 m is:
PE = mgh = 150 kg * 9.8 m/s^2 * 45 m
The kinetic energy of the body when it reaches the ground will be equal to the potential energy at that height, since there is no additional energy input or loss during free fall.
Therefore, KE = PE = 150 kg * 9.8 m/s^2 * 45 m
Now, we can find the velocity (v) using the formula for kinetic energy (KE = 1/2 * mv^2), where v is the velocity.
1/2 * mv^2 = 150 kg * 9.8 m/s^2 * 45 m
Simplifying the equation:
v^2 = (150 kg * 9.8 m/s^2 * 45 m) / (1/2 * 150 kg)
v^2 = 9.8 m/s^2 * 45 m * 2
v^2 = 882 m^2/s^2
Taking the square root of both sides:
v = √882 m/s
So, the velocity of the body on impact will be approximately 29.7 m/s.