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Raindrops. If the effects of the air acting on falling raindrops are ignored, then we can treat raindrops as freely falling objects. (a) Rain clouds are typically a few hundred meters above the ground. Estimate the speed with which raindrops would strike the ground if they were freely falling objects. Give your estimate in $\mathrm{m} / \mathrm{s}, \mathrm{km} / \mathrm{h},$ and milh. (b) Estimate (from your own personal observations of rain the speed with which raindrops actually strike the ground. (c) Based on your answers to parts (a) and (b), is it a good approximation to neglect the effects of the air on falling raindrops? Explain.

a) 60 $\mathrm{m} / \mathrm{s}$$=| 134 \mathrm{mi} / \mathrm{h}$b) From personal observation, it is reasonable to believe that raindrops travel at 9 $\mathrm{m} / \mathrm{s}$ . This happens due to air resistance. The acceleration of the raindrop increases when it falls from certain height and also air resistance on the drop increases continuously. If the resistive force due to air on the rain drop is equal to the weight of the rain drop, then the speed of the rain drop remains constant.c) It is not a good approximation to neglect the effects of the air on failing raindrops. Air resistance slows raindrops considerably so that they do not travel in the estimated of 60 $\mathrm{m} / \mathrm{s}$ andrather around 1 $\mathrm{m} / \mathrm{s}$ .

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

Cornell University

University of Sheffield

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 here we're going to say that rain jobs dropped from a height of 200 meters. You can use any height, but 200 muses about approximately the height from with Dick, from which they drop from so part is asking us to find the final velocity. So B y final squared equals V Y initial squared plus two, two g delta y again, these rain jobs condense in clouds so initially they they do not have any initial velocity in the white direction. And we can say that V Y final equals two g delta y to the 1/2 power we're going to solve and say This is going to be equal to two times 9.8 times, 200 to the 1/2 power and we get that V Y final equals 62.61 meters per second. Now we're going to find this in kilometers per hour, so 62.61 meters per second for every one kilometer. There are one thousand two meters and there are 36 100 seconds for every one hour. So we can say that this is going to be equal to 225 o'clock, 225 0.4 kilometers per hour. So we simply want to express this in meters per second kilometers per hour and lastly, miles per hour. So we can say that 60 2.61 meters per second for every one mile. There are 1,609 meters and then there are 36 100 seconds in one hour and this is giving us 140 0.1 miles per hour. Now, Part B is asking Is out there saying that based on observation, how fast to rain jobs usually hit the ground and when they usually hit the ground, they usually hit the ground with the speed of the equals one meter per second and you can see this. They have nowhere near these velocities when they hit the ground. In fact, even though it's a tiny mass, they would have much more kinetic energy and if they were to drop it this speed, it would ah be very painful to stand and rain. However again they do drop it around one meter per second as they hit the ground, and this is just based on observation. So exactly. So what exactly is happening? Well, it's a poor assumption to neglect a resistance. So it is a poor assumption to neglect a resistance on a falling rain jock. It's going to reach its terminal velocity way before it hits the ground. Um, and although the thermodynamics of the thermal dynamics of ah, sorry the aerodynamics of a range up might not seem to significant, they would. They do have a significant impact on how fast these raindrops fall. So it is a poor assumption. Teo neglect a resistance on falling raindrops. They will reach terminal velocity long before hitting the ground. That is the end of the solution. Thank you for watching.

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