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Chapter 1: Q9CP (page 17)

(a) A unit vector lies in the plane, at an angle of from theaxis, with a positivecomponent. What is the unit vector? (It helps to draw a diagram.) (b) A string runs up and to the left in theplane, making an angle of to the vertical. Determine the unit vector that points along the string.

Short Answer

Expert verified
  1. The unit vector is .
  2. The unit vector is .

Step by step solution

01

Definition of unit vector

A vector is a quantity that has both a magnitude and a direction associated with it. A unit vector is a vector with a magnitude of one. Unit vectors form the basis of vector calculus.

Unit vector given by the direction cosines is .

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Most popular questions from this chapter


Question: you throw a ball. assume that the origin is on the ground, with the+y axis pointing upward. Just after the ball leaves your hand its position is0.06,1.03,0m . The average velocity of the ball over the next 0.7sis 17,4,6m. As time 0.7safter the ball leaves your hand, what is the height of the ball above the ground?

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

0.0

(0,0,0)

B

1.0

(22.3,26.1,0)

C

2.0

(40.1,38.1,0)

a) What is the average velocity of the ball as it travels between location A and location B? b) If the ball continued to travel at the same average velocity during the next second, where would it be at the end of that second? (That is, where would it be at time t=2s )c) How does your prediction from part b) compare to the actual position of the ball at t=2s(location C)? If the predicted and the observed location of the ball are different, explain why?

Which of the following observers might observe something that appears to violate Newton's first law of motion? Explain why. (1) A person standing still on a street corner (2) A person riding on a roller coaster (3) A passenger on a starship traveling at 0.75c toward the nearby star Alpha Centauri (4) An airplane pilot doing aerobatic loops (5) A hockey player coasting across the ice.

(a) Powerful sports car can go from zero to 25 m/s (about 60mi/h) in 5 s. (1) What is the magnitude of average acceleration? (2) How does this compare with the acceleration of a rock falling near the Earth’s surface? (b) Suppose the position of an object at time t is <3+5t,4t2,2t-6t3>. (1) what is the instantaneous velocity at time t? (2) What is the instantaneous acceleration at time t? (3) What is the instantaneous velocity at time t=0? (4) What is the instantaneous acceleration at time t=0?

Here are the positions at three different times for a bee in flight (a bee’s top speed is about 7 m/s ). Time6.3s6.8s7.3sPosition<-3.5,9.4,0>m<-1.3,6.2,0>m<0.5,1.7,0>m(a)Between 6.3 s and 6.8 s , what was the bee’s average velocity? Be careful with signs.

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