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A rocket blasts off vertically from rest on the launch pad with a constant upward acceleration of 2.50 $\mathrm{m} / \mathrm{s}^{2} .$ At 20.0 $\mathrm{s}$ after blastoff, the engines suddenly fail, and the rocket begins free fall. (a) How high above the launch pad will the rocket eventually go? (b) Find the rocket's velocity and acceleration at its highest point. (c) How long after it was launched will the rocket fall back to the launch pad, and how fast will it be moving when it does so?

a) 628 $\mathrm{m}$b) 9.8 $\mathrm{m} / \mathrm{s}^{2}$ downwardc) $=\sqrt{36.42 \mathrm{s}}$$=111 \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

University of Washington

Simon Fraser University

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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with a positive life. Tto be upwards now There are two periods off constant acceleration oneness A light to be 2.5 meters per seconds. Caf while the engines fire on then my acceleration will be negative 9.8 meters per second Scratch then the engines Shut it off on both of these arts accelerations are constant at during these times, so we can use constant acceleration in questions within each period. So basically during this period and this video now for the first part So they find a speak and hide at the end of the first 20 seconds, something is equal to during the seconds um, you will lose a right to be 2.5 minutes of the second. Scared two on initial velocity is Siegel fund. Initial height is also single. Now find the final velocity with loose the secretion. Since we have all the ban emitters on the wrist off the pan emitters to solve for rib eye. So we directly plugged them into this equation and we get this velocity to be 15 meters a second Mom for height, the videos this accretion over here because the same for the same reason we have all the perimeters needed to solve this equation. And we get this value of height or right to be 500 meter next considered awash in from this point, the maximum height. So for that we have I not could be 500 meter because ah, we're starting from this point now. So now uh, why not will be 500 meters ve knocked. Lee will be not this than you. 15 meters per second on our maximum height Velocity zero. So vai is zero now and obviously acceleration is now negative 9.8 meters per second squared now we saw these equations to find the maximum height of it is why so yes, move to the next. It's for that. So use desecration now Since we don't have, they have no idea about the time taken to travel this distance. And we need to solve for heights of the secretions both at this also From this we can write why minus why not equal do this value and we solve this for the perimeters we have for the for the second motion on DH, This gives us 1 20 This means that divided the equal. Why not less one during the igniter on why Lord is as you can see, here is 500 meters So why will be 6 28 meter now the dietician off this part off the motion it is time could be found from This is a question the same that we used here I'm from here We can find an expression for time he solved it for the values we have on DH this time comes out, comes out to the 5.10 seconds the second But now at the highest point We know that velocity zero because ah, it comes to, ah moment that relate guns to arrest and then falls down again. But at that instant the Y issue on it why is obviously 9.8 meters per seconds downward And if you are taking positive, I access Toby upward. Then you can write a burrito. The negative nine point meter per second Scared Aziz We didn't disgrace and the part But so consider the motion from the maximum height back to the ground. So we have Why not? Which is the maximum height And is he called the 6 28 meter? Because we are considering the motion from the maximum height. So the ground so final hide will be serial because it's on the ground now off the city. Not why is here? Because at maximum, I, uh, thought it comes momentarily to arrest. So we're not white. Is Siegel on? Obviously, acceleration is acceleration due to gravity of it is negative. 9.8 meter scare the negative sinus because it positive it points in the negative I direction. Now we will solve for this aggression and I appeal. And this will give us time. Basically, despite goes of it because we not buy you see it all now time will be equal toe twice off my minus. Why not over a guy and you have to take root over that because ofthe squared Come over here. He solved us and they find this timeto 11.3 seconds. So the total time off the rocket in air. This is quite a while. 20 seconds. Which is the stein? Less five point one serial seconds. That is the time taken by it to travel from this point. So jungle drums this point. So the maximum height. So this is the time plus time taken. Buy it toe. Come backto the ground from the maximum ID. So this time so we add them all on We get the total time it spends in air. So this is equal to 36.4 seconds on DH final velocities and it comes back with the ground just before it hits the ground. It is equality. So we solve. This equation is angry not quite of the seal a guy to be negative 9.8 meters squared and timeto element on three seconds like we just found out now. And this gives velocity to be negative on 13 meet up a second. So just before it hits the ground, the rocket will have a speed off 111 meters per second and off this little point in on the downward direction and therefore the negative science, which makes sense

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