How do you find maxium height when a ball is hit from a height of 0.08m and has a intial velocity of +7.5 m/s straight up?
To find the maximum height reached by a ball that is hit straight up, you can use the equations of motion for vertical motion.
Step 1: Identify the given information:
- Initial height (h0) = 0.08m
- Initial velocity (v0) = +7.5 m/s (upwards)
- Acceleration due to gravity (g) = -9.8 m/s^2 (downwards)
Step 2: Identify what you need to find:
- Maximum height (h)
Step 3: Choose the appropriate equation:
The equation that relates the initial velocity, final velocity, acceleration, and displacement in vertical motion is:
v^2 = v0^2 + 2gh
In this case, you know the initial velocity (v0) and the acceleration (g). You need to find the maximum height (h), which is the displacement (Δh) from the initial height (h0) to the maximum height.
Step 4: Solve the equation for the desired variable:
Rearrange the equation to solve for h:
h = (v^2 - v0^2) / (2g)
Step 5: Substitute the known values into the equation and calculate:
Substitute the known values into the equation:
h = (0^2 - 7.5^2) / (2 * -9.8)
Calculate the result:
h ≈ (-56.25) / (-19.6)
h ≈ 2.8676 m
The maximum height reached by the ball is approximately 2.87 meters above the initial height of 0.08 meters.