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" | katex }} with initial velocity {{ "v_0" | katex }}, it follows a parabolic path. The maximum height is reached when the vertical component of velocity becomes zero.

Formula

The maximum height {{ "h_{max}" | katex }} can be calculated using:

{{ "h_{max} = \\frac{v_0^2 \\sin^2(\\theta)}{2g}" | katex }}

Where:

{{ "v_0" | katex }} = initial velocity (m/s)
{{ "\\theta" | katex }} = launch angle (degrees)
{{ "g" | katex }} = acceleration due to gravity (9.81 m/s²)

Solution Steps

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

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

Projectile Motion Maximum Height Quiz

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