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Chapter 3: Q2P (page 57)

A displacement vector r→in the xy plane is long and directed at angle θ=30°in Fig.3-26 . Determine (a) the x component and (b) the y component of the vector1.

Short Answer

Expert verified

The x component of r→is 1.5 m

The y component of r→is 7.5 m

Step by step solution

01

Step 1: Calculation for x component of vector r→

Each component of a vector represents a split of the vector. The components of a vector could be computed if the vector is split along each of the axes. Here trigonometric functions and the given magnitude of vectors are used to find components of the vector.

Given the displacement vector r→is 15 m and the direction of vector is θ=30°.

The x and y components of the vector a are given by the following equations.

rx=rcosθ(1)ry=rsinθ(2)

Substituting the values of r→and θin equation (i), the x component is calculated as,

rx=15m×cos(30°)=15m.

02

Step 2: Calculation for y component of vector r→

Substituting the values of r→and θin equation (ii), the x component is calculated as,

ry=15m×sin(30°)=7.5m

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Most popular questions from this chapter

Here are two vectors:

a→=(4.00m)i⏜-(3.00m)j⏜b→=(6.00m)i+(8.00m)j

What are (a) the magnitude and (b) the angle (relative to i ) of a→? What are (c) the magnitude and (d) the angle of b→? What are (e) the magnitude and (f) the angle of a→+b→;(g) the magnitude and (h) the angle of b→-a→; and (i) the magnitude and (j) the angle ofrole="math" localid="1656943686601" a→-b→? (k) What is the angle between the directions of b→-a→anda→-b→?

IfF⇀=q(v⇀xB⇀)andv⇀is perpendicular toB⇀, then what is the direction of B in the three situations shown in Fig. 3-24 when constant q is (a) positive and (b) negative?

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In Fig. 3-30, a vector awith a⇀magnitude of 17.0mis directed at angle 56.0°counterclockwise from the +x axis. What are the components (a)and (b) ayof the vector? A second coordinate system is inclined by angle θ=18.0°with respect to the first. What are the components (c)axand (d) ayin this primed coordinate system?

In the product F→=qv→×B→, takeq=2,v→=2.0i⏜+4.0j⏜+60k⏜,andF→=4.0i⏜-20j⏜+12k⏜. What then isB→in unit-vector notation ifBx=By?
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