Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(III) A motorboat traveling at a speed of 2.4 $\mathrm{m} / \mathrm{s}$ shuts offits engines at $t=0 .$ How far does it travel before comingto rest if it is noted that after 3.0 $\mathrm{s}$ its speed has dropped tohalf its original value? Assume that the drag force of thewater is proportional to $v$ .

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$$10 \mathrm{m}$$

Physics 101 Mechanics

Chapter 5

Using Newton's Laws: Friction, Circular Motion, Drag Forces

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Cornell University

Hope College

University of Winnipeg

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

03:53

Suppose that a motorboat i…

08:17

A tugboat pulls a small ba…

01:10

'Ihe deceleration exp…

05:44

A motorboat cuts its engin…

01:11

03:41

A motorboat coasts toward …

we're gonna talk about draft force. So we need to remember that when we have a body that's moving on the surface off, let's say any liquid, for example, the water. But it could actually be any fluid. So, for example, if you're moving on the air, you experience a drag force. So suppose that this body here is moving forward with a speed V. Then the drag force F will be pointing in the opposite direction and usually the force in Britain as miners, because it's in the opposite direction, a constant times the velocity. In our case, we have a motor boat whose initial speed is 2.4 m per second. And we know that after a time of three seconds, the velocities have So we uh huh t whose three seconds his vizier over to Okay, eso in question? A. Ah, what we need to do is to calculate how far the boat travels before coming to rest. So before V is equal to 0 m per second us and what we need to remember is that the force is equal to the mass times declaration. The exploration is devi the team, and here since the motion is one dimensional. I'm not gonna give it vector treatment. I mean, just and all right, the force and the velocity as scale er's so have that The forces m d v d t. And we know that it's equal to mine as a constant times the velocity V yeah, s. So what I'm gonna do is to right this as Devi, divided by V, is able to minus view Graham times DT. And I'm going to integrate on both sides. We know that. And I'm going to wait from Time t zero to t We know that when she is equal to zero, the velocity is V zero. And when she is equal to cheat with 0/2 mhm. Uh, but I'm just gonna leave it a za functional V. Um, And after that, I'm gonna, um said t go to three. So have the natural algorithm off. V divided by zero. This is the first Integral is able to minors be over, um, times t. So I'm gonna exponentially eight on both sides. We have V divided by zero with minus actually. Sorry. This is e to the minus. B T 0 g. So v is equal to the zero e to the minus B t a gram. Okay. Thesis is an important formula. I'm gonna highlight it. Okay. Um, now, notice that we have t equals three seconds is equal to 0/2. Now we went is equal to three seconds is with zero e to the minus three B over em. And this is the 0/2, So e to the minus three of you over m is one half. Okay. Eso if we take a lotta rhythm on both sides, we get that three b over em. Is the logarithms off to meaning? That's Buba. Ram is the logarithms to over three, and then you hear him right is equal. Choose your 0.23. Okay, uh, this should be in one of her second. So I'm gonna Why are they in here? Seconds to the minus. Warm. Okay, so now we need to find what is the value off the attacks? So remember that V is V zero e to the minus B t a gram. Now we is DX dy t. So this is V zero e to the minus B Children. So the X is zero e to the minus B to Bram the T and I'm gonna integrate. Move side from T equals zero thio T and from Mexico to x zero two x To have no tax is equal to V zero times minus AM Overbey times e to the minus B t over AM minus one. Okay, so deep Delta X is equal to M V zero Overbey one minus Z to the minus B t over. Um Okay, Now notice that for the velocity to be equal to zero in our formula here she has to go to infinity. Then V is equal to zero so the object will come to rest at time T equals infinity. Eso Let's see how far the motorboat traveled when t goes to infinity So that's acts for t go into infinity is equal to m v zero Overbey times one Since this term here is just oh, it tends to zero v zero is 2.4 meters per second and then we have two divided by be divided by am so that 0.23 seconds to the minus one So Doubter acts is equal to 10 approximately 10 m which concludes the rights yourself Yes,

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:09

The earth magnetic field is 5 X 10 s T. How fast would you have to drive you…

01:14

00310.0 pointsConsider the light rays depicted in the figure.Wha…

09:47

Case 2 An ideal monatomic gas of 2.8 moles is held in a perfectly insulated …

01:06

17. At what depth in seawater is the gauge pressure equal to atm? The densit…

01:46

An object 3.0 cm high is placed 20.0 cm from a convex mirror with a focal le…

01:15

1. Two substances mercury with a density 13600 kglm3 and glucose with a dena…

02:42

Question 9 (5 points) A capacitor in a series RC circuit is charged to 60% o…

02:05

Question 7 (5 points) A car battery with a 12-V emf and an internal resistan…

Question 6 (5 points) 'parallel-plate capacitor filled with a material …

06:16

2. (a) If the position of a particle is given by X= 20t-5t2, where X is in m…