A stone is dropped from a height of 10 m on an unknown planet having g = 20 m/s2.

Calculate the speed of the stone when it hits the surface of the planet. Also calculate the
time it takes to fall through this height

V^2 = Vo^2 + 2g*h = 0 + 40*10 = 400

V = 20 m/s.

0.5g*t^2 = 10 m.
10*t^2 = 10
t^2 = 1
t = 1 s.

Or
V = Vo + g*t = 20
V = 0 + 20t = 20
t = 1 s.

To calculate the speed of the stone when it hits the surface of the planet, we can use the equation for free fall motion:

v = u + gt

Where:
v = Final velocity (speed of the stone when it hits the surface)
u = Initial velocity (0 m/s since the stone is dropped)
g = Acceleration due to gravity on the planet (20 m/s^2)
t = Time taken to fall through the height

Since the stone is dropped, the initial velocity is zero, so the equation simplifies to:

v = gt

Substituting the values into the equation, we have:

v = 20 m/s^2 * t

Now let's calculate the time it takes to fall through the height of 10 m. We can use another formula of motion:

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

Where:
s = Height (10 m)
u = Initial velocity (0 m/s)
g = Acceleration due to gravity (20 m/s^2)
t = Time taken

Substituting the values into the equation, we have:

10 m = 0 * t + (1/2) * 20 m/s^2 * t^2

Simplifying the equation further, we get:

10 m = 10 m/s^2 * t^2

Dividing both sides by 10 m/s^2, we have:

t^2 = 1

Taking the square root of both sides, we have:

t = 1 s

Therefore, the time taken to fall through a height of 10 m is 1 second.

Now, substituting the value of t in the first equation to find the final velocity:

v = 20 m/s^2 * 1 s

v = 20 m/s

Therefore, the speed of the stone when it hits the surface of the planet is 20 m/s.