A ball of mass 8 kg is thrown vertically upward from the ground , with an initially velocity of 25 m/s. Determine the maximum height to which it will travel if atmospheric resistance is neglected.
h = 25t-4.9t^2
max height at t = 25/9.8 = 2.55
h(2.55) = 25*2.55 - 4.9*2.55^2 = 31.89m
To determine the maximum height reached by the ball, we can use the concepts of projectile motion. The maximum height is achieved when the ball's velocity becomes zero at the highest point of its trajectory.
Here are the steps to calculate the maximum height:
Step 1: Identify the given information:
- Mass of the ball (m) = 8 kg
- Initial velocity (u) = 25 m/s
- Acceleration due to gravity (g) = 9.8 m/s² (assuming no atmospheric resistance)
Step 2: Determine the time taken to reach the highest point:
The initial velocity (u) is the velocity at the ground level, and at the maximum height, the final velocity (v) becomes zero. We can use the following kinematic equation to find the time (t) it takes:
v = u + at
Since we know the final velocity (v) is zero at the highest point, the equation becomes:
0 = u - gt
Solving for t:
t = u / g
Substituting the values:
t = 25 m/s / 9.8 m/s²
Step 3: Calculate the maximum height (h):
To find the maximum height (h), we can use another kinematic equation:
h = ut + (1/2)gt²
Substituting the values:
h = 25 m/s × (25 m/s / 9.8 m/s²) + (1/2) × 9.8 m/s² × (25 m/s / 9.8 m/s²)²
After simplifying the expression, compute the equation to find the maximum height.