rocket.png

Rocket

Theme A - Space, Time & Motion

thermometer.png

Thermometer

Theme B - The Particulate Nature Of Matter

water-wave.png

Water Wave

Theme C - Wave Behaviour 

magnifying-glass-tilted-right.png

Magnifying Glass Tilted Right

Theme D - Fields

microscope.png

Microscope

Theme E - Nuclear & Quantum Physics

So you think physics is boring? Well, think again! This time, we&#39;re stepping out of the boring straight-line world and exploring things that fly, leap, and plummet. Yes, we&#39;re looking at projectile motion in two-dimensions!

Imagine you&#39;re a baseball player and you&#39;ve thrown a baseball straight up with an initial speed we&#39;ll call U. Don&#39;t worry about the wind messing with your throw; we&#39;re in a world without air resistance for now. The baseball, from the moment it&#39;s released, feels the pull of gravity, slowing it down until it pauses for a split second at the top of its journey, then zooms back down, returning to your glove at the same speed it started.

&nbsp;

In this situation, the path or trajectory the baseball follows is a straight line up and down, almost like it&#39;s playing peekaboo with the sky. Graphically, if we were to plot this journey over time, we&#39;d get something like a mountain peak for the displacement-time graph, and a valley for the distance-time graph.

Now, how do we make sense of this motion? Well, you can use suvat equations, introduced earlier. SUVAT is just a fancy acronym where each letter stands for a property in physics:

<ul>
	<li>S is for displacement</li>
	<li>U is for initial velocity</li>
	<li>V is for final velocity</li>
	<li>A is for acceleration</li>
	<li>T is for time</li>
</ul>

In our baseball scenario, the initial vertical speed is U, the time to the peak is T, the maximum height is H, and the acceleration due to gravity is -g. Gravity gets a negative sign because it&#39;s acting in the opposite direction to our upward throw.

&nbsp;

Here are some SUVAT equations that can be used for vertical motion

<ul>
	<li>Final Velocity = Initial Velocity - Gravity * Time (v = u - gt)</li>
	<li>Displacement = Initial Velocity * Time - 0.5 * Gravity * Time2 (s = ut - 0.5gt2)</li>
	<li>Final Velocity2 = Initial Velocity2 - 2 * Gravity * Displacement (v2 = u2 - 2gs)</li>
</ul>

Remember that the total time for the baseball to go up and then back down is just 2T.

Let&#39;s put our knowledge to the test with a couple of real-world examples.

Example : A student drops a stone into a well and hears it splash 2.3 seconds later. Ignoring the time it takes for the sound to reach her, we can calculate

<ul>
	<li>The depth of the well -&nbsp;Using our SUVAT equation (s = ut + 0.5gt2), we find the depth is 26m.</li>
	<li>The speed at which the stone hits the water -&nbsp;We can use v = u + gt, which gives us \(\frac {23m}{s}\).</li>
	<li>Why we can ignore the time sound takes to travel -&nbsp;Sound travels at around \(300 \frac {m}{s}\), so the time to cover 25m would only be 0.08s. This is just 4% of the total time taken for the stone to fall, so it&#39;s barely noticeable!</li>
</ul>

Example : A hot-air balloon is rising vertically at a steady\(5.0 \frac {m}{s}\). An object is dropped from the balloon when it&#39;s 30m above the ground. This situation is a bit more complex, but with our understanding of physics, we can certainly work it out!

&nbsp;

So, next time you throw a baseball or watch a hot-air balloon, remember - there&#39;s physics in action!

&nbsp;

(Note: The solutions to the hot-air balloon problem are not provided in the source text, hence it is left as an exercise for the reader.)

Understanding 2D Projectile Motion: Beyond Basics

ib-higher-level.webp

Higher Level

Physics HL

Theme A - Space, Time & Motion

Understanding 2D Projectile Motion: Beyond Basics

Table of content

The vertical hop

Unlock the Full Content!

Theme A - Space, Time & Motion

Understanding 2D Projectile Motion: Beyond Basics

Table of content

The vertical hop

Unlock the Full Content!