A stone of 8 kg mass falls from the top of an 80 m-high building. Find the velocity of the stone when it reaches the ground
Oh boy, we've got a stone falling! This is like the Olympics for rocks. So, let's calculate its velocity when it hits the ground using some physics, shall we?
We can start by using the formula to calculate the final velocity of the stone in free fall, which is v = √(2gh). In this formula, "g" represents the acceleration due to gravity (which is about 9.8 m/s² on Earth), and "h" is the height from which the stone is dropped.
Plugging in the numbers, we have v = √(2 * 9.8 m/s² * 80 m). Let me get my calculator out, so we can crunch some numbers.
Doing the math, we find v = √(1568) m/s, which simplifies to v ≈ 39.60 m/s (approximately).
So, the stone reaches the ground with a velocity of around 39.60 m/s. That's quite the speedy rock!
To find the velocity of the stone when it reaches the ground, we can use the equations of motion.
First, we can use the equation for the final velocity (V) to calculate the velocity at the ground. The equation is:
V^2 = u^2 + 2as
Where:
V = final velocity
u = initial velocity (which is 0, since the stone starts from rest)
a = acceleration due to gravity (which is approximately 9.8 m/s^2)
s = displacement (which is the height of the building, 80 m)
Plugging in the values, the equation becomes:
V^2 = 0 + 2 * 9.8 * 80
V^2 = 0 + 1568
V^2 = 1568
To find V, we take the square root of both sides:
V = sqrt(1568)
V ≈ 39.58 m/s
Therefore, the velocity of the stone when it reaches the ground is approximately 39.58 m/s.
To find the velocity of the stone when it reaches the ground, you can use the equations of motion.
1. Start by finding the time it takes for the stone to fall to the ground. You can use the equation:
h = 0.5 * g * t^2
where h is the height of the building (80 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes for the stone to fall.
Rearrange the equation to solve for t:
t^2 = (2 * h) / g
t^2 = (2 * 80) / 9.8
t^2 ≈ 16.33
t ≈ sqrt(16.33)
t ≈ 4.04
2. Now that you have the time, you can find the velocity using the equation:
v = g * t
where v is the velocity of the stone and t is the time calculated in step 1.
Substituting the values:
v = 9.8 * 4.04
v ≈ 39.79 m/s
So, the velocity of the stone when it reaches the ground is approximately 39.79 m/s.
V^2 = Vo^2 + 2g*d
Vo = 0
g = +9.8 m/s^2
d = 80 m.
Solve for V.