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(1) Estimate $(a)$ how long it took King Kong to fall straightdown from the top of the Empire State Building $(380 \mathrm{m}$high $),$ and $(b)$ his velocity just before landing.

a) $t=8.8$ secondsb) $86 \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 2

Describing Motion: Kinematics in One Dimension

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

University of Washington

Simon Fraser 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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we want to know about King Kong falling off the Empire State Building. And since we have an initial height of 380 meters and a final height is the grounds that zero R Delta Y in this case is why minus y zero. So that means it zero minus 380 which actually gives us a negative displacement, which makes sense because we're falling down. And so we're looking for the time it takes for him to fall this far. And so we can use this equation be zero t What's 1/2 A T squared and a couple things you need to sort out be Zero is what you're starting at is zero meters per second. Because you're not moving, you're just jumping off. And we also know that a this minus g. So let's just start solving this. Um, the V zero is gonna v zero cheese term is going to go away. So we're ending up with zero t minus 1/2 GT squared. We get Delta. Why cools minus 1/2 GT squared, which makes sense because the negatives will cancel or lift with minus 3 80 equals minus 1/2 times 9.8 squared. Do the math. Forget t squared. It's about 77.55 That means T is 8.8 seconds. And we also want to know velocity it before King Kong gets the ground. Ah, so then we can use we're looking for Final Velocity. This is gonna equal initial velocity plus 80. So it's gonna equal initial velocity. Zero a is minus g is Okay, so we'll say negative 9.80 times. What's R t? 8.8 seconds and our final velocity. Here we get a negative number because we're going down, uh, 86.24 But we want to know just the speed, so it ends up being 86.24 meters per second. And the only reason this negative is because when we hit the ground or velocity is pointing in this direction and so that makes the vector negative. But we just want the magnitude, and that's 86.24 meters per second

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