a stone of mass 0.7kg is projected vertically upward with a speed of 5m/s .calculate the Hm reach
kinetic energy becomes potential energy ... 1/2 m v^2 = m g h
h = v^2 / (2 g)
To calculate the maximum height reached by the stone, we can use the equations of motion.
We know that the initial velocity (u) is 5 m/s, final velocity (v) is 0 m/s (at the maximum height), acceleration (a) is -9.8 m/s^2 (considering downward acceleration due to gravity), and we need to find the height (Hm).
We can use the equation:
v^2 = u^2 + 2aHm
Substituting the given values:
0^2 = 5^2 + 2(-9.8)Hm
0 = 25 - 19.6Hm
Simplifying the equation:
19.6Hm = 25
Hm = 25 / 19.6
Hm ≈ 1.28 meters
Therefore, the stone reaches a maximum height of approximately 1.28 meters.
To calculate the maximum height reached by the stone, you can use the equations of motion.
First, determine the initial velocity of the stone when it is projected vertically upward:
Initial velocity (u) = +5 m/s (Note: Since the stone is going upward, the velocity is positive.)
Next, find the acceleration due to gravity (g):
Acceleration due to gravity (g) = 9.8 m/s^2 (taking it as positive, since it opposes the upward motion of the stone)
Using the second equation of motion, which relates displacement (s), initial velocity (u), acceleration (a), and time (t):
s = u*t + (1/2)*a*t^2
In this case, the stone is projected upward until it reaches its maximum height, so its final velocity (v) will be zero. Thus, we can set v = 0 in the equation, and solve it for the displacement (s) to find the maximum height.
0 = 5 - 9.8*t (Substituting u = 5 m/s and a = -9.8 m/s^2 into the equation)
9.8t = 5
t = 5 / 9.8 ≈ 0.51 seconds
Now, substitute this value of time (t) back into the equation of motion to find the displacement (s):
s = 5 * 0.51 + (1/2) * (-9.8) * (0.51)^2
s ≈ 1.27 meters
Therefore, the maximum height reached by the stone is approximately 1.27 meters.