A stone of mass 0.7kg is projected vertically upward with a velocity 5m/s. Calculate the height attained. g=10m/s2
The mass does not matter.
v = 5 - 10t
max height is when v=0
h(t) = 5t - 5t^2
so plug in t = 1/2
or, max h is (v^2-1)/(2g)
To calculate the height attained by the stone, we can use the equations of motion.
The initial velocity (u) is given as 5 m/s, and the acceleration due to gravity (g) is given as 10 m/s². The mass of the stone (m) is given as 0.7 kg.
First, we need to find the time taken (t) for the stone to reach its maximum height. We can use the equation:
v = u + gt
where v is the final velocity (which will be 0 m/s at the maximum height).
0 = 5 + (10)(t)
Rearranging the equation, we find:
10t = -5
t = -0.5 s
Note that since the stone is projected upward, we use the negative sign in the equation to indicate its upward motion.
Next, we can use the equation:
s = ut + (1/2)gt²
where s is the height attained.
Plugging in the values:
s = (5)(-0.5) + (1/2)(10)(-0.5)²
s = -2.5 + (0.5)(0.25)
s = -2.5 + 0.125
s = -2.375 m
The height attained by the stone is -2.375 m. Since height cannot be negative, we take the magnitude of the height.
Therefore, the stone attains a height of 2.375 m.
To calculate the height attained by the stone, we can use the laws of motion and the given information.
We know that the stone is projected vertically upward with an initial velocity of 5 m/s. The acceleration due to gravity is given as 10 m/s^2, acting in the downward direction.
Initially, let's assume the height attained by the stone as H.
We can use the kinematic equation for motion in the vertical direction:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0 m/s when the stone reaches its highest point)
u = initial velocity (5 m/s in the upward direction)
a = acceleration due to gravity (-10 m/s^2 in the downward direction)
s = displacement or height attained (H)
Substituting the given values into the equation:
0^2 = (5^2) + 2 * (-10) * H
0 = 25 - 20H
20H = 25
Dividing both sides of the equation by 20:
H = 25 / 20
H = 1.25 meters
Therefore, the height attained by the stone is 1.25 meters.