If stone is thrown directly down ward from the top of a 40m tall building with an initial speed of 10m/s,what will be the speed of the stone,when it reach the ground?g 10N/kg
You don't say what the mass of the stone is, unless you are hinting that it is 1kg. (If you take g=10)
In any case, its initial PE is 10mg=100m, and its initial KE is (1/2)(m)(10^2) = 50m
So, at the bottom, its energy is all KE, in the amount of 150m = 1/2 m v^2, so v = √300
v = Vi + a t
Vi = -10
a = -9.81
v = -10 - 9.81 t
h = Hi + Vi t + (1/2) a t^2
0 = 40 - 10 t - 4.9 t^2
4.9 t^2 + 10 t - 40 = 0
https://www.mathsisfun.com/quadratic-equation-solver.html
t = 2 seconds
so
v = -10 - 9.81(2)
= - 29.6
V^2 = Vo^2+2g*h = 10^2+20*40 = 900
V = 30 m/s.
Firdt you answer my question
To find the speed of the stone when it reaches the ground, we can use the equations of motion for uniformly accelerated motion.
The equation that relates distance, initial velocity, final velocity, acceleration, and time is:
s = ut + (1/2)at^2
Where:
- s = distance (in this case, the height of the building, which is 40m)
- u = initial velocity (10m/s)
- a = acceleration (acceleration due to gravity, which is approximately 9.8m/s^2)
- t = time taken to reach the ground (which we want to find)
- v = final velocity (which we want to find)
In this case, the stone is thrown downward, so we take the acceleration due to gravity as a negative value.
Plugging the given values into the equation, we have:
40m = (10m/s)t + (1/2)(-9.8m/s^2)t^2
Simplifying the equation, we get:
-4.9t^2 + 10t - 40 = 0
To find the value of t, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
Where a = -4.9, b = 10, and c = -40.
Plugging these values into the quadratic formula, we get:
t = (-10 ± √(10^2 - 4(-4.9)(-40))) / (2(-4.9))
Simplifying further, we get:
t = (-10 ± √(100 - 784)) / -9.8
t = (-10 ± √(-684)) / -9.8
Since we are dealing with time, we can ignore the negative square root since time cannot be negative. Therefore, we have:
t = (-10 + √(-684)) / -9.8
Simplifying further, we get:
t ≈ 3.2 seconds
Now that we have found the time taken to reach the ground, we can find the final velocity using the equation:
v = u + at
Plugging in the values, we get:
v = 10m/s + (-9.8m/s^2)(3.2s)
Simplifying, we find:
v ≈ -31.4m/s
Since we are dealing with velocity, the negative sign indicates that the stone is moving downward. So, the speed of the stone when it reaches the ground is approximately 31.4 m/s.