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Two coconuts fall freely from rest at the same time, one from a tree twice as high as the other. (a) If the coconut from the taller tree reaches the ground with a speed $V$ , what will be the speed (in terms of $V$ ) of the coconut from the other tree when it reaches the ground? (b) If the coconut from the shorter tree takes time $T$ to reach the ground, how long (in terms of $T )$ will it take the other coconut to reach the ground?

a) $\frac{V}{\sqrt{2}}$b) $\sqrt{2} T$

Physics 101 Mechanics

Chapter 2

Motion along a Straight Line

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

University of Michigan - Ann Arbor

Hope College

McMaster University

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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So we have a coconut falling from a tree and it has a The tree has a height of H. The coconut has a velocity of V, and the time it takes for the coconut to reach the ground takes time. T Then we have a coconut rather weaken sake. Coconut falling from shorter tree. And this will have a height of h. The coconut love the velocity of the and the time it takes for the coconut to reach the ground will equal capital T. We also know that Ah, the heights of thie. Taller coconut is two times the height of the shorter coconut halves of short a coconut tree. So we can say that V squared equals the initial squared plus two g age. And we can say that the initial squared is going to be equal to zero because they're the coconut has no initial velocity, and he is going to be equal to for kimchi H to the 1/2 power. We can say that V squared equals the initial squared plus to G. H. And we can say that V is going to be equal to to G H to the 1/2 power So if we were to divide these weaken savy over V is going to be equal to radical two. Or we can say that the velocity is going to be equal to the over radical too. So the velocity of the shorter tree will be equal to the velocity of the taller tree divided by radical too. Now they want the time as well. So we can say that H equals the initial T plus 1/2 g T square and this is going to be equal to two h so we can say that T is going to be equal to radical for H over G. We can also say that H equals the initial T plus 1/2 G capital t squared. And so we can say that capital T will be equal to radical to H over G. And so we can say that if we divide the two tea over t, this equals radical too, and so t will equal t radical to essentially. This means that the time it takes for the coconut to reach the ground from the taller tree lower case T equals the time it takes for the coconut to reach the ground from the shorter tree times a radical too. Ah, that is the end of the solution. Thank you for watching.

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