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.