A stone of mass 0.5kg is thrown vertically upwards with a velocity of 10ms
if g = 9.81 m/s^2
v = 10 - 9.81 t
v = 0 at top
t = 10/9.81 = 1.02 seconds upward
h = Hi + Vi t - 4.9 t^2
at top if Hi = 0 at ground
h = 0 + 10 * 1.02 - 4.9*1.02^2 = 10.2 - 5.1 = 5.1 meters high at top
To solve the problem, we need to determine the maximum height achieved by the stone and the time it takes to reach that height.
Step 1: Let's start by identifying the information given in the problem:
- Mass of the stone (m) = 0.5 kg
- Initial vertical velocity (u) = 10 m/s (upwards)
Step 2: Using the given information, we can now find the time taken to reach the maximum height using the formula:
v = u + at
Since the stone is thrown vertically upwards, the final velocity (v) at maximum height will be equal to 0 m/s. We can assume the acceleration due to gravity (g) as -9.8 m/s² (taking gravity to be acting in the opposite direction). Rearranging the formula, we get:
0 = 10 + (-9.8)t
Simplifying the equation:
-9.8t = -10
t = -10 / -9.8
t ≈ 1.02 seconds
So, it takes approximately 1.02 seconds for the stone to reach its maximum height.
Step 3: Now, let's calculate the maximum height using the formula:
v² = u² + 2as
At maximum height, the final velocity (v) is 0 m/s, the initial velocity (u) is 10 m/s, and the acceleration (a) is -9.8 m/s² (taking gravity to be acting in the opposite direction). We need to find the displacement (s). Rearranging the formula, we get:
0 = 10² + 2(-9.8)s
Simplifying the equation:
-196s = -100
s = -100 / -196
s ≈ 0.51 meters
Therefore, the stone reaches a maximum height of approximately 0.51 meters.
To find the maximum height reached by the stone, we can use the equations of motion and the principles of classical mechanics.
1. First, let's determine the initial vertical velocity (u) of the stone. The given information states that the stone is thrown vertically upwards with a velocity of 10 m/s. Therefore, u = 10 m/s.
2. Second, we need to find the acceleration (a) acting on the stone. In this case, we can assume that the only force acting on the stone is gravity, which has a constant acceleration of approximately 9.8 m/s^2 directed downwards. Therefore, a = -9.8 m/s^2 (negative sign indicates that the acceleration is directed opposite to the direction of motion).
3. Now, we can use the equation of motion to determine the time taken for the stone to reach the maximum height. The equation is given by: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since the stone reaches its maximum height, its final velocity (v) will be zero. Substituting the known values, we get: 0 = 10 - 9.8t. Solving for t gives: t = 10 / 9.8 ≈ 1.02 seconds.
4. Finally, we can find the maximum height (h) reached by the stone using the equation: h = ut + (1/2)at^2. Substituting the known values, we get: h = (10)(1.02) + (1/2)(-9.8)(1.02)^2 ≈ 5.10 meters.
Therefore, the stone reaches a maximum height of approximately 5.10 meters.