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Lesson_1.3_Homework_Solution

# Lesson_1.3_Homework_Solution - Lesson 1.3 Homework...

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Lesson 1.3 Homework Solutions 1. A bear walks northeast for 12 m and then east for 12 m. Show each displacement graphically and find the resultant displacement vector. 12 m Northeast vector can be written as 12 cos 45 i + 12 sin 45 j = 8 . 5 i + 8.5 j 12 m East vector = 12 i The resultant of these vectors = 8.5 i + 8.5 j + 12 i = 20.5 i + 8.5 j The magnitude of the resultant = 22 20.5 8.5 22.2 m += The angle θ the resultant makes with the positive x axis is given by 8.5 tan 0.41 20.5 y x θ == = . Therefore, θ = tan -1 0.41 = 22.3 o . 1 2 m n o r t h - e a s 12 m east . 22.3 o 2. Find the rectangular components of a vector v that has a magnitude of 12 ms -1 and is oriented at an angle 37 o with the positive x-axis. x-component = 12 cos 37 o = 9.6 m.s -1 y-component = 12 sin 37 o = 7.2 m.s -1 3. A vector A has an x-component -4.5 m and a y-component 2.2 m. What is the magnitude and direction of vector A?

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The magnitude of vector A is: 22 4.5 2. 50 2 . N A =+ = The angle θ vector makes with the x-axis is: 1 2.2 tan 26 4.5 154 26 180 o o θ == = = −+ 154 o 2.2 m -4.5 m A 4. Find the resultant of the following vectors: 30 o o 45 o 20 N 15N 25 N B C The three vectors can be written in component form as: A = 20 cos 45 o i + 20 sin 45 o j = 14.14 i + 14.14 j B = 25 cos 150 o i + 25 sin 150 o j = -21.65 i + 12.5 j C = 15 cos 300 o i + 15 sin 300 o j = 7.5 i – 12.99 j
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Lesson_1.3_Homework_Solution - Lesson 1.3 Homework...

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