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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

A cat rides a merry-go-round turning with uniform circular motion. At time t1=2.00s, the cat’s velocity is v⇀1=(3.00m/s)i^+(4.00m/s)j^, measured on a horizontal xy coordinate system. Att2=5.00s , the cat’s velocity is v⇀2=(-3.00m/s)i^+(-4.00m/s)j^.What are (a) the magnitude of the cat’s centripetal acceleration and (b) the cat’s average acceleration during the time intervalt2-ti, which is less than one period?

The three vectors in Fig. 3-33 have magnitudes a=3.00m,b =4.00 m, and c =10.0 mand angle θ=30.0°What are (a) the x component and (b) the y component ofa→;(c) the x component and (d) the y component of b; and (e) the x component and (f) the y component ofc→? Ifc→=pa→+qb→what is the value of (g) pand q?

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=‐3.8,cz=‐6.1;dx=4.4,dy=‐2.0,dz=3.3

Which of the following are correct (meaningful) vector expressions? What is wrong with any incorrect expression?

(a) A→⋅(B→⋅C→)               (f) A→+(B⃗×C⃗)(b)A→×(B→⋅C→)              (g) 5+A→(c)A→⋅(B→×C→)              (h) 5+(B→⋅C→) (d)A→×(B→×C→)          (i) 5+(B→×C→)(e) A→+(B→⋅C→)              (j) (A→⋅B→)+(B→×C→)

Two beetles run across flat sand, starting at the same point, Beetle one runs 0.50mdue east, then 0.80mat 30°north of due east. Beetle two also makes two runs; the first is 1.6mat 40°east due to north. What must be (a) the magnitude and (b) direction of its second run if it is to end up at the new location of beetle 1?
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