UNIT: CATAPULT

ACT-Based Math: Measuring Launch Angles & Distances

OBJECTIVE:

Students use trigonometry to calculate launch angles and distances.

Materials Needed:

Ruler

Protractor

Meter stick

Catapult

Target board

Calculator

Student Directions:

Goal:
You will conduct a hands-on experiment with a catapult to measure projectile distances at different launch angles. Then, you will apply trigonometric functions (sine and cosine) to calculate expected horizontal distances and compare them to your results.

Step 1: Set Up Your Materials

Gather all materials: catapult, protractor, ruler, meter stick, target board, and calculator.

Make sure you’re working in a clear, open space where you can safely launch projectiles.

Step 2: Adjust the Launch Angle

Using the protractor, adjust your catapult to the following angles:

30°, 45°, and 60°

Double-check the angle before launching to ensure accuracy.

Step 3: Launch and Measure

For each angle:

Launch the projectile 3 times.

Use the meter stick to measure how far the projectile travels from the launch point to where it lands (horizontal distance).

Record all 3 distances for each angle in a data table.

Calculate the average distance for each angle and add it to your table.

Sample Data Table:

Angle (°)	Trial 1 (m)	Trial 2 (m)	Trial 3 (m)	Average Distance (m)
30°
45°
60°

Step 4: Calculate Expected Distance Using Trigonometry

Assume a constant initial velocity (provided by your teacher or measured during class).

Use the following formula to calculate horizontal distance (range) without air resistance:

Sample Comparison Table:

Angle (°)	Expected Distance (m)	Actual Average Distance (m)	Difference (m)
30°
45°
60°

Step 5: Analyze and Discuss

As a group, discuss the following question:

"Why does 45° typically produce the farthest horizontal distance in projectile motion?"

Consider the math behind the sine of 2θ, and how horizontal and vertical components of motion affect range.

ACT-STYLE QUESTION:

A student launches a projectile at a 60° angle with an initial velocity of 10 m/s. What is the horizontal distance traveled if air resistance is negligible?

8.66 m

10 m

5 m

7.5 m