PS.1.2 Shooting the apple solution

TL;DR

To hit a falling apple with a projectile, aim directly at the apple's location at the moment of firing.

Transcript

PROFESSOR: So in this example, we want to hit an apple hanging from a tree with a projectile. And the main point of the problem is to figure out at what angle to the ground should we aim our projectile when we fire it off in order to hit the apple. And in this example, we're assuming that the apple drops from the tree at the same instant that we fi... Read More

Key Insights

• 💩 The angle at which a projectile should be launched to hit a falling apple is determined by considering the kinematics of both objects.
• 🍍 The apple and the projectile fall vertically at the same rate, resulting in a collision if the projectile is launched directly at the apple's location.
• 💦 If the apple doesn't drop or if it starts dropping before the projectile is fired, adjustments need to be made to the angle or initial velocity of the projectile.

Questions & Answers

Q: What is the main objective of the problem discussed in the video?

The main objective is to determine the angle at which to launch a projectile in order to hit a falling apple.

Q: How does the kinematics of the apple and the projectile differ?

The apple drops vertically and only its vertical position changes, while the projectile has both horizontal and vertical motion due to its initial velocity.

Q: How is the time of collision, capital-T, calculated?

The time of collision is calculated by subtracting the horizontal distance traveled by the projectile from the horizontal distance between the projectile and the apple.

Q: What adjustments would need to be made if the apple doesn't drop or if it starts dropping before the projectile is fired?

If the apple doesn't drop, a different angle for the projectile needs to be chosen to hit the apple directly. If the apple starts dropping before the projectile is fired, the initial vertical velocity of the apple needs to be considered in the kinematics equations.

Summary & Key Takeaways

• The problem is to determine the angle at which a projectile should be launched in order to hit a falling apple.

• The kinematics of both the projectile and the apple are considered to find the time and distance of the collision.

• If the apple doesn't drop or if it starts dropping before the projectile is fired, the angle of the projectile needs to be adjusted.