Mt. Everest is more than 8000 m high. How fast would an object be moving if it could free fall to sea level after being released from an 4750-m elevation? (Ignore air resistance)

How would I solve this?

To solve this problem, you can use the principles of physics and equations of motion. The object is initially at an elevation of 4750 m and will fall freely to sea level, which is 0 m. Since we're ignoring air resistance, the only force acting on the object is gravity.

The first step is to determine the time it takes for the object to fall from 4750 m to 0 m. We can use the equation of motion for free fall:

s = ut + (1/2)gt^2

Where:
s = displacement (difference in elevation) = 4750 m - 0 m = 4750 m
u = initial velocity (0 m/s, as the object is released from rest)
g = acceleration due to gravity ≈ 9.8 m/s^2
t = time taken

Substituting the known values into the equation, we get:

4750 = 0 + (1/2)(9.8)t^2

Simplifying the equation, we have:

4750 = 4.9t^2

Dividing both sides by 4.9:

t^2 = 4750 / 4.9

t^2 ≈ 969.39

Taking the square root of both sides:

t ≈ √969.39

t ≈ 31.14 seconds

So, it would take approximately 31.14 seconds for the object to fall from the 4750-m elevation to the sea level.

To calculate the final velocity of the object, we can use another equation of motion for free fall:

v = u + gt

Where:
v = final velocity
u = initial velocity (0 m/s)
g = acceleration due to gravity ≈ 9.8 m/s^2
t = time taken (31.14 seconds)

Substituting the values:

v = 0 + (9.8)(31.14)

v ≈ 305.17 m/s

Therefore, if the object could free fall from a 4750-m elevation to sea level, ignoring air resistance, it would be moving at approximately 305.17 m/s when it reaches sea level.

To solve this problem, we can use the equations of motion under free fall. The object will initially have gravitational potential energy at its starting point and will convert it into kinetic energy as it falls towards sea level.

The equation for gravitational potential energy is given by:
PE = mgh

Where:
PE is the gravitational potential energy,
m is the mass of the object,
g is the acceleration due to gravity,
h is the height of the object.

The equation for kinetic energy is given by:
KE = (1/2)mv^2

Where:
KE is the kinetic energy,
m is the mass of the object,
v is the velocity of the object.

In this case, since the object is in free fall, the potential energy at the starting point will be fully converted into kinetic energy at the landing point. Therefore, we can equate the gravitational potential energy at the starting point to the kinetic energy at the landing point:

mgh = (1/2)mv^2

Since mass (m) cancels out, we can solve for velocity (v) using the equation:

v = sqrt(2gh)

Now, let's substitute the given values into the equation.

Given:
h = 4750 m
g = 9.8 m/s^2

Plugging these values into the equation, we have:

v = sqrt(2 * 9.8 m/s^2 * 4750 m)

Now, we can calculate the velocity:

v = sqrt(94000 m^2/s^2)

v ≈ 306.19 m/s

Therefore, an object would be moving at approximately 306.19 m/s if it could free fall from a 4750-m elevation to sea level, ignoring air resistance.