A Body with a mass of 150kg is located at a height of 45 m. If allowed to fell freely to the ground. What will be its velocity on impact?
KE= 1/2*m*v^2
PE= m*g*h
1/2*m*v^2= m*g*h
1/2*150kg*45m*v^2= 150kg*9.81*45m
3375* v^2= 66217.5
3375*v^2/3375= 66217.5/3375
v^2= 19.62m/s
Is this done correctly?
There are a lot more steps than you need.
V = sqrt(2 g h)
Forget about the mass.
I do not agree with your V^2 number. You have 45 meter height terms on both sides of your equation. That is wrong.
You have to use both potential energy and kinetic energy formulas since they are mutually convertible.
potential energy= mass(150) x gravity(9.81) x height(45m)
=66,217.5
plug that number into the following equation...
ke= 1/2 x mass x velocity^2
*remember pe = ke
66,217.5= 1/2 x 150 x v^2
132435=150 x v^2
882.9=v^2
29.713=v
the velocity will be 29.71 when the rock hits the floor. Utilize both formulas :)
Yes, your calculations are correct. Plugging in the values correctly, you have correctly solved for the velocity on impact. The final result, v^2 = 19.62 m/s, represents the squared velocity. To find the actual velocity, you will need to take the square root of this value, v = √19.62 m/s, which is approximately 4.43 m/s.
Yes, your calculations are correct. To find the velocity on impact, you correctly set the equation for the conservation of mechanical energy by equating the kinetic energy (KE) to the potential energy (PE). Then, substituting the given values, you solve for the velocity (v).
However, there is a minor error in your calculation when dividing both sides of the equation by 3375 to isolate v^2. The correct equation should be:
v^2 = 66217.5 / 3375
v^2 = 19.62
Taking the square root of both sides, you find:
v ≈ 4.43 m/s
So, the object will have a velocity of approximately 4.43 m/s when it impacts the ground.