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Chapter 3: Q10P (page 57)

Find the (a)x, (b)y, and (c)zcomponents of the sum of the displacements and whose components in meters are cx=7.4,cy=鈥�3.8,cz=鈥�6.1;dx=4.4,dy=鈥�2.0,dz=3.3

Short Answer

Expert verified

a) x component of isc+dis12m

b) y component of isc+dis鈥�5.8m

c) z component of isc+dis鈥�2.8m

Step by step solution

01

To calculate x component in meters

c and d are the displacement vectors. The sum of these vectors gives a resultant. Here the components of the resultant are to be found.

Given are the x, y z, components of the displacements c and d respectively.

cx=7.4,cy=-3.8,cz=-6.1,dx=4.4,dy=-2.0,dy=3.3,

The resultant of sum of displacements is given by

R=c+dRx=cx+dxiRy=cy+dyiiRz=cz+dziii

Substituting the above components in equation (i), the x component of R can be written as

Rx=7.4+4.4Rx=12m

02

To calculate y component in meters

Ry=-3.8-2.0Ry=-5.8m

03

To calculate z component in meters

Rz=-6.1+3.3Rz=-2.8m

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Most popular questions from this chapter

A room has dimensions 3.00m(height)脳3.70脳4.30m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) Could the length of its path be less than this magnitude? (c) Greater? (d) Equal? (e) Choose a suitable coordinate system and express the components of the displacement vector in that system in unit-vector notation. (f) If the fly walks, what is the length of the shortest path? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.)

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