A body of mass 2kg is released from rest and falls freely under gravity.find it's speed when it has fallen a distance of 10m
v^2 = 2gs = 2*9.8*10
v is downward
To find the speed of the body when it has fallen a distance of 10m, we can use the equations of motion under gravity.
Step 1: Determine the acceleration due to gravity.
The acceleration due to gravity on the Earth is approximately 9.8 m/s^2. We will use this value in our calculations.
Step 2: Calculate the time taken to fall 10m.
We can use the equation of motion, s = ut + (1/2)at^2, where:
s = distance fallen = 10m
u = initial velocity = 0 (as it is released from rest)
a = acceleration due to gravity = 9.8 m/s^2
t = time
Using the equation, we can rearrange it to solve for t:
10 = 0*t + (1/2)*9.8*t^2
10 = 4.9t^2
Simplifying the equation, we have:
t^2 = 10/4.9
t^2 = 2.04
Taking the square root of both sides, we find:
t = √(2.04)
t ≈ 1.43 seconds
Step 3: Calculate the final velocity.
The final velocity can be found using the equation v = u + at, where:
v = final velocity
u = initial velocity = 0 (as it is released from rest)
a = acceleration due to gravity = 9.8 m/s^2
t = time taken to fall 10m = 1.43 seconds
Plugging in the values, we get:
v = 0 + 9.8 * 1.43
v ≈ 14.014 m/s
Therefore, the speed of the body when it has fallen a distance of 10m is approximately 14.014 m/s.
To find the speed of the body when it has fallen a distance of 10m, we can use the equations of motion.
In this case, the body is falling freely under gravity, so we can use the equations of motion for uniformly accelerated motion. The key equation we will use is:
v^2 = u^2 + 2as
Where:
- v is the final velocity (speed) of the body
- u is the initial velocity (initial speed) of the body
- a is the acceleration of the body
- s is the distance traveled by the body
In this scenario, the body is released from rest, so its initial velocity u is zero.
The acceleration due to gravity, denoted by g, is approximately 9.8 m/s^2 on Earth. So we can substitute the values into the equation:
v^2 = 0 + 2 * 9.8 * 10
Simplifying the equation:
v^2 = 196
To solve for v, we take the square root of both sides:
v = √196
v ≈ 14 m/s
Therefore, the speed of the body when it has fallen a distance of 10m is approximately 14 m/s.