A 3 kg object falls from a height of 10 m. What is its velocity just before it hits the ground? How would this problem differ if the object falling from a height of 10 m only had a mass "m"?

PE=KE

mgh=mv²/2
v=sqrt(2gh)

To find the velocity of the object just before it hits the ground, we can use the equation of motion.

The equation we can use is the second equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity (which is 0 in this case because the object starts from rest)
a = acceleration due to gravity (-9.8 m/s^2 for objects falling near the surface of the Earth)
s = distance fallen (which is 10 m in this case)

Plugging in the given values into the equation, we get:

v^2 = 0 + 2(-9.8)(10)
v^2 = -196
v = √(-196)

Since velocity can't be negative in this case, the negative sign indicates that the object is moving in the opposite direction (upwards). Therefore, we take the positive square root:

v = 14 m/s

So, the velocity of the 3 kg object just before it hits the ground is 14 m/s.

Now, let's consider the case where we have a mass "m" instead of a 3 kg object. In this case, the mass of the object would affect the force of gravity acting on the object but not the acceleration due to gravity. Therefore, the equation to find the velocity would remain the same:

v^2 = u^2 + 2as

However, the mass "m" would replace the 3 kg value in the equation. The value of "m" would then be used to find the force of gravity using the equation:

F = mg

Where:
F = force of gravity
m = mass of the object
g = acceleration due to gravity (-9.8 m/s^2)

Once the force of gravity is determined, it can be substituted into the equation to find the velocity of the object just before it hits the ground.