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Chapter 1: 13P (page 39)

Question: What is the magnitude of the vector v, where v=(8×106,0,-2×107)m/s?

Short Answer

Expert verified

Answer

Magnitude of given vector is 21.54×106m/s

Step by step solution

01

Formula used

Magnitude of a vector ahaving coordinates (x,y,z)is given by|a|=x2+y2+z2. The magnitude of a vector gives the length of the vector so, basically magnitude is used to find the length of a vector between the initial and the final point of the vector.

02

Calculation of magnitude

Substitute x=8×106,y=0and z=-2×107into the formula of magnitude to get the magnitude of the given vector.

|v|=(8×106)2+02+(-2×107)2=(64×1012)+0+(4×1014)=464×1012=21.54×106m/s

Thus, the magnitude of the given vector vis 21.54×106m/s.

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The first stage of giant Saturn V rocket reached a speed of 2300 m/s at 170 s after lift-off.

(a) What was the average acceleration in m/s/s?

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Figure 1.60 shows the trajectory of a ball travelling through the air, affected by both gravity and air resistance.

Here are the positions of the ball at several successive times.

Location

t(s)

Position ( m)

A

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B

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C

2.0

(40.1,38.1,0)

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What is the result of multiplying the vectora→by the scalar f, wherea→=<002,-1.7,300>and f = 2.0?
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