05 Projectile Motion

05 April

Simulation of Projectile Motion with Air Resistance

Seng Kwang Tan 03 Motion and Forces, 05 Projectile Motion, IP3 03 Dynamics, Simulations 0 Comments
Open in new tab 🔗 This simulation offers a hands-on and dynamic way to explore the physics of projectile motion with and without air resistance. By adjusting parameters such as launch velocity, angle, and air resistance, users can visualize how these factors affect the shape and reach of a projectile’s trajectory. The app provides real-time changes including motion paths, velocity vectors, and a velocity-time graph showing horizontal and vertical components separately. It also calculates and displays key quantities such as maximum height and range under ideal and non-ideal conditions (based on an arbitrary coefficient of drag. Through interactive experimentation and visual reinforcement, learners gain a deeper understanding of concepts the effect of air resistance, and the difference between theoretical and real-world motion. This is suitable for JC1’s topic on projectile motion. It can also be used for Upper Sec, if you change the launch angle to 90 degrees.
12 July

Pressure and Projectile – Penguin’s Poop

Seng Kwang Tan 05 Projectile Motion, 12 Temperature and Ideal Gases 0 Comments

An interesting paper on the range of penguin’s poop. Their motivation? “Such information is useful for keepers to avoid the direct hitting of faeceses.”

Source: https://arxiv.org/pdf/2007.00926.pdf?fbclid=IwAR2Y6CkFXeCrJH7nxf624To8RcpdRSs0e3_COto9ev6MK-Z_wnObeRHvVlg

06 April

2-Dimensional Kinematics Problem: Shooting a dropping coconut

Seng Kwang Tan 05 Projectile Motion 0 Comments

The following is a question (of a more challenging nature) posed to JC1 students when they are studying the topic of kinematics.

A gun is aimed in such a way that the initial direction of the velocity of its bullet lies along a straight line that points toward a coconut on a tree. When the gun is fired, a monkey in the tree drops the coconut simultaneously. Neglecting air resistance, will the bullet hit the coconut?

coconut kinematics
Two-Dimensional Kinematics: Gun and Coconut Problem

It is probably safe to say that if the bullet hits the coconut, the sum of the downward displacement of coconut $$s_{yc}$$ and the upward displacement of the bullet $$s_{yb}$$ must be equal to the initial vertical separation between them, i.e. $$s_{yc}+s_{yb}=H$$

This is what we need to prove.

Since $$s_{yc}=\frac{1}{2}gt^2$$

$$s_{yb}=u\text{sin}\theta{t}-\frac{1}{2}gt^2$$ and $$s_{xb}=u\text{cos}\theta t$$

$$s_{yc}+s_{yb}=u\text{sin}\theta{t}=u\text{sin}\theta\times \frac{s_{xb}}{u\text{cos}\theta}=s_{xb}\times{\text{tan}\theta}$$

At the same time, the relationship between $$H$$ and the horizontal displacement of the bullet $$s_{xb}$$ before it reaches the same horizontal position of the coconut is $$\text{tan}\theta=\frac{H}{s_{xb}}$$

Hence, $$s_{yc}+s_{yb}=H$$