A mass makes a projectile motion on a table (like the one in the projectile motion experiment) with inclination angle of the table as α=6o. The initial velocity and the initial angle are is 100 cm/s and 30 deg. respectively. What is the maximum height hmax ? (sin(6)=0.1, cos(6)=0.995, sin(30)=0.5, cos(30)=0.87, g=10 m/s2)
To find the maximum height (hmax) of the projectile motion, we can use the following equation:
hmax = (V₀² * sin²(θ)) / (2 * g)
Here's how we can calculate it step-by-step:
Step 1: Given values
- V₀ (initial velocity) = 100 cm/s
- θ (initial angle) = 30 degrees
- α (angle of the table) = 6 degrees
- g (acceleration due to gravity) = 10 m/s²
Step 2: Convert the given values to the appropriate units
- V₀ = 100 cm/s = 100/100 m/s = 1 m/s
- θ = 30 degrees
- α = 6 degrees
Step 3: Calculate the maximum height (hmax)
hmax = (V₀² * sin²(θ)) / (2 * g)
= (1² * sin²(30)) / (2 * 10)
= (1 * (0.5)²) / 20
= (0.25) / 20
= 0.0125 m
So, the maximum height (hmax) of the projectile motion is 0.0125 meters or 1.25 cm.