a small brick mass 700 g is projected vertically downwards at a velocity of 1,25(m/s) from the top of a building of height 25m.calculate the magnitude of the velocity at which the brick hits the ground?
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To calculate the magnitude of the velocity at which the brick hits the ground, we need to use the equations of motion.
First, we can calculate the time it takes for the brick to fall from the top of the building to the ground using the equation:
h = (1/2) * g * t^2
where h is the height of the building (25m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Solving for t in the above equation, we get:
t^2 = (2h) / g
t^2 = (2 * 25) / 9.8
t^2 = 5.1
Taking the square root of both sides, we get:
t ≈ 2.26 seconds
Now, we can calculate the final velocity of the brick when it hits the ground using the equation:
v = u + gt
where u is the initial velocity (1.25 m/s), g is the acceleration due to gravity (9.8 m/s^2), and t is the time (2.26 seconds).
v = 1.25 + (9.8 * 2.26)
v ≈ 23.548 m/s
Therefore, the magnitude of the velocity at which the brick hits the ground is approximately 23.548 m/s.
To calculate the magnitude of the velocity at which the brick hits the ground, we can use the equations of motion. Specifically, we can use the equation that relates the final velocity (v), initial velocity (u), acceleration (a), and distance (s):
v^2 = u^2 + 2as
In this case, the brick is projected vertically downwards, so the initial velocity (u) is 1.25 m/s, the final velocity (v) is what we're trying to find, the acceleration (a) is the acceleration due to gravity (-9.8 m/s^2 since it is acting in the opposite direction), and the distance (s) is the height of the building, which is 25 m.
Substituting the known values into the equation:
v^2 = (1.25)^2 + 2(-9.8)(25)
v^2 = 1.5625 - 490
v^2 = -488.4375
Since velocity cannot be negative, we can conclude that there is an error in our calculation. It seems that the brick is not able to go through the entire distance of 25m with an initial velocity of 1.25 m/s. Please check if there are any other details mentioned in the question that might be relevant for the calculation.