Chapter 6: Q38P (page 215)

Jack & Jill are maneuvering a $3000 K g$ boat near a dock. Initially the boat’s position is $(2, 0, 3)$ and its speed is 1.3m/s . As the boat moves to position (4,0,2). Jack exerts a force (-400, 0, 200) N and Jill exert a force and Jill exert a force (150,0,300)N . (a) How much work does jack do? (b) How much work does Jill do? (c) Without doing any calculations, say what is the angle between the (vector) force that Jill exert, and the (vector) velocity of the boat. Explain briefly how you know this (d) Assuming that we can neglect the work done by the water on the boat, what is the final speed of the boat?

Short Answer

Expert verified

a. Jack does -1000J work.

Step by step solution

Given data

Mass of the boat, m = 3000 kg.
The initial position of the boat, $(x_{i}, y_{i}, z_{i}) = (2, 0, 3) m$ .
The initial speed of the boat, $v_{i} = 1.3 m / s$ .
Final location of the boat, $(x_{f}, y_{f}, z_{f}) = (4, 0, 2) m$ .
Force exerted by Jack, $\vec{F_{J a c k}} = (- 400, 0, 200) N$ .
Force exerted by Jill, $\vec{F_{J i l l}} = (150, 0, 300) N$ .

Introduction

A vector quantity means the physical quantity which has same directionsas well as magnitude.

Solution

The work done by a constant force $\vec{F}$ :

Acting through a displacement $△ \vec{r}$ is given by

$W = \vec{F} . △ \vec{r}$

The displacement vector of the boat is given by

$△ \vec{r} = (x_{f}, y_{f} z_{f}) - (x_{i}, y_{i}, z_{i}) △ \vec{r} = [(- 400, 0, 200) N] [(2, 0, - 1)] △ \vec{r} = [(- 800 + 0 - 200) J] △ \vec{r} = - 1000 J$

It is negative because the boat’s position is opposite.

Hence, Jack does -1000J work.

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