Projectile Motion - Maximum Height

This quiz tests your understanding of projectile motion, specifically calculating the maximum height reached by a projectile.

Key Concepts

When a projectile is launched at an angle $\theta$ with initial velocity $v_0$, it follows a parabolic path. The maximum height is reached when the vertical component of velocity becomes zero.

Formula

The maximum height $h_{max}$ can be calculated using:

$h_{max} = \frac{v_0^2 \sin^2(\theta)}{2g}$

Where:

• $v_0$ = initial velocity (m/s)
• $\theta$ = launch angle (degrees)
• $g$ = acceleration due to gravity (9.81 m/s²)

Solution Steps

1. Find the vertical component of initial velocity: $v_{0y} = v_0 \sin(\theta)$
2. Apply the kinematic equation at maximum height where $v_y = 0$
3. Use $v_y^2 = v_{0y}^2 - 2gh$
4. Solve for h when $v_y = 0$

Tips

• Remember to convert angles from degrees to radians when using trigonometric functions
• The maximum height depends only on the vertical component of the initial velocity
• At maximum height, the projectile has only horizontal velocity