Investigating Projectile Motion Revision Notes for HSC SSCE Physics

Investigating Projectile Motion

Introduction to experimental projectile motion

Studying projectile motion in a practical setting presents unique challenges. One of the main difficulties is achieving consistent, repeatable results. When throwing a ball by hand, it's nearly impossible to maintain the same speed and angle for each throw. This is why investigations typically require a projectile launcher to ensure reproducibility.

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Various types of launchers can be used, such as tennis ball launchers (commonly used for sports practice) or similar devices. While it's possible to construct your own launcher, safety must always be the top priority.

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Safety Warning: Projectile launchers can be extremely dangerous. Only use low-powered launchers with soft projectiles to minimise risk. Never point launchers at people or fragile objects.

In this investigation, you will collect measurements from a launched projectile and use these to reconstruct its trajectory. The trajectory represents the complete path the projectile follows through the air.

Investigation 2.2: Trajectory of a projectile

Aim

To plot the trajectory of a projectile by measuring its motion and calculating velocity components at different points during flight.

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Before beginning, you should formulate a hypothesis or develop an inquiry question. For example: "How does the launch angle affect the trajectory and range of a projectile?"

Materials required

Tennis ball launcher (or similar projectile launcher)
Tennis ball
Chalk dust
Stopwatch
Large tape measure (minimum 30 m length)
Large protractor
Extension cord and power source for the launcher

Risk assessment

Before conducting any practical investigation, it's essential to identify potential hazards and plan how to manage them safely.

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Risks you should consider:

Stand clear of the launcher when firing
Trip hazards from equipment and cables
Projectile bouncing unpredictably after landing
Eye injury from projectile or chalk dust

Manage these by keeping the work area tidy, wearing safety glasses if necessary, and maintaining awareness of your surroundings.

Method

Follow these steps carefully to collect accurate data:

1. Test the launcher by firing the ball several times to estimate the range. Choose a landing area where the ball will leave a visible chalk mark, such as a concrete surface.

2. Measure the launch angle ( $\theta$ ) using the protractor. This is the angle between the launch tube and the horizontal ground.

3. Coat the ball lightly with chalk dust so it will mark the landing point clearly.

4. Fire the ball from the launcher.

5. Use the stopwatch to measure and record the time of flight. Remember to include the uncertainty in your measurement. The uncertainty will be larger than just the reading error from the stopwatch (typically around $\pm 0.2$ s for reaction time).

6. Measure the horizontal range from the launcher to the chalk mark where the ball first contacted the ground. Record this measurement with its uncertainty.

7. Adjust the launcher to a different angle and repeat steps 1-6. Perform this twice more so you have three complete sets of data at different angles.

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Optional extension: If you have access to a high frame rate video camera, you can record the flight and analyse the footage to make additional measurements.

Results

Record your measurements systematically as you collect them. Use a table format to keep your data organised:

This table has space for three trials at different launch angles. You will measure the first three rows directly (launch angle, range, time of flight) and calculate the remaining values during your analysis.

Analysis of results

Complete the results table by performing the following calculations. Remember to show your working and state any assumptions clearly.

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Analysis Task 1: Calculate maximum height and initial vertical velocity

Use the measured time of flight to determine:

The maximum height ( $h$ ) reached by the tennis ball
The initial vertical velocity ( $u_y$ )

Assumption to state: The ball takes equal time to rise to maximum height and fall back down (symmetrical trajectory).

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Analysis Task 2: Calculate initial velocity components from range

Use the measured horizontal range and launch angle to find:

The initial horizontal velocity ( $u_x$ )
The initial vertical velocity ( $u_y$ )

Assumption to state: Air resistance is negligible, so horizontal velocity remains constant.

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Analysis Task 3: Determine total initial velocity

Draw a vector diagram showing the horizontal and vertical components of velocity. Use vector addition (Pythagoras' theorem) to calculate the total initial velocity ( $u$ ):

$u = \sqrt{u_x^2 + u_y^2}$

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Analysis Task 4: Calculate velocities at different trajectory points

Determine the velocity and its components at:

The top of the trajectory (maximum height)
The end point (just before landing)

For each point, find:

Horizontal velocity component
Vertical velocity component
Total velocity magnitude

Key assumption: At the highest point, vertical velocity = 0, but horizontal velocity remains constant throughout.

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Analysis Task 5: Create scale trajectory diagrams

Draw accurate scale diagrams of the trajectory for each launch angle, similar to Figure 2.9 shown below:

Your diagrams must include:

A clearly marked scale (e.g., 1 cm = 2 m)
The maximum height ( $h$ ) marked and labelled
The horizontal range ( $x_{\text{max}}$ ) marked and labelled
Velocity values at three key points: start, peak, and end
Vector arrows showing velocity components at these three points
The launch angle ( $\theta$ ) clearly indicated

Discussion

Analyse your results by considering these questions:

1. Compare the three trajectories you created. How do the velocity components change throughout the flight? What patterns do you notice?

2. You calculated initial vertical velocity two different ways (from time of flight and from range/angle). Do these values agree? Consider the uncertainties when making your comparison.

3. Evaluate the validity of your assumptions. Were they reasonable? How might violations of these assumptions affect your results?

4. Suggest specific improvements to the investigation method or propose extensions to explore further aspects of projectile motion.

5. Answer your original inquiry question or state whether your hypothesis was supported by the evidence.

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Critical Analysis Points:

Always compare calculated values with their uncertainties before drawing conclusions
Consider how air resistance (which we ignored) would affect real trajectories
Think about which measurements contribute most to the overall uncertainty

Conclusion

Write a summary that:

Restates the aim
Summarises key findings
Comments on the validity of results
Addresses your hypothesis or inquiry question

Key concepts

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Important points to remember about investigating projectile motion:

Projectile motion can be investigated experimentally using a projectile launcher and suitable projectile
Safety is paramount - projectiles can move very fast and cause serious injuries
The velocity of a projectile and its horizontal and vertical components can be calculated from measured values (range, time of flight, launch angle) using kinematic equations
The standard projectile motion model assumes no air resistance, making it an approximation of real motion

Understanding check

Test your knowledge with these questions:

1. Why do we assume a projectile travels the same horizontal distance before and after reaching peak height? If this assumption is incorrect due to air resistance, in which part of the trajectory does the projectile travel further horizontally?

2. In an experiment, Ali measures the time of flight as $3.52 \pm 0.02$ s. Calculate:

The maximum height of the trajectory
The uncertainty in this calculated value
State your assumptions clearly

3. Using the time of flight from Question 2, calculate:

The initial vertical velocity
The uncertainty in this value

Remember!

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Key Points to Remember:

Reproducibility is key: Use a mechanical launcher rather than throwing by hand to get consistent results
Safety first: Always use soft projectiles and low-powered launchers in open areas
Measure carefully: Record uncertainties for all measurements - they're essential for evaluating your results
Show your assumptions: Always state what you're assuming (e.g., no air resistance, symmetrical trajectory)
Vector thinking: Projectile motion has independent horizontal and vertical components that must be analysed separately and then combined

Investigating Projectile Motion (HSC SSCE Physics): Revision Notes