Suppose you start at the origin, move along the x-axi distance of 4 units in the positive direction, and then downward a distance of 3 units. What are the coordin of your position?
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- Figure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.Help | System Announcements Z Your answer is partially correct. Try again. For the vectors in the figure, with a = 3.60, b = 2.7o, and c = 4.50, calculate (a) a b, (b) a.2, and (c) b.7. (a) Number This answer has no units v Units (b) Number14.02 This answer has no units v Units (c) Number This answer has no units v Units Click if you would like to Show Work for this question: Open Show Work arch1. Two points in the æy plane have Cartesian coordinates (2.00, –4.00) m and (-3.00, 3.00) m. Determine (a) the distance between these points and Answer + (b) their polar coordinates. Answer
- 3. Let a, b, n be integers, with n > 0. Prove that a = b (mod n) if and only if a² + b² = 2ab (mod n²).1,076 :6: F1 If a vector A has components Ax>0, and Ay<0, then the angle that this vector makes with the positive X-axis must be in the range O a. 0° to 90°. 148,433 @ 2 W S b.90° to 180°. O c. 180° to 270°. mand O d.270° to 360°. O e. cannot be determined without additional information X -8° F2 - # 3 E D 31 21 80 F3 C $ 4 R F a F4 % 5 tv e F5 T G 6 V B Ad !! c F6 Y H (2982 & 7 F7 U N 8 J DII F8 1 M WA 9 K F9 O A ) O A F10 L P command | ' F11 1 { C optioQuestion: The polar coordinates of a point are 50m and . Then, what are its Cartesian coordinates? A. 2.75i+ 4.763j m, B. -2.75i- 4.763j m, C. 2.75i - 4.763j m, D. 4.763j m, E. -2.75i + 4.763j m,
- Given two vectors that starts from the origin: A = 2i – 7j and B = I – 3j – 5k. What is the length of vectors AB? a. -i + 4j – 5k b. 3i – 10j – 5k c. 3i + 4j – 5k d. None of the above6. The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to $(r) =, where r = Vx² + y², r2+ equi- potential lines of the potential function is _(accurate to two decimal places).1. If vectors P = (2i+ 3j+ 6k) cm and Ŕ = (10i - 5j+ 10k) cm, then what is the A. sum of P and Ŕ? B. difference between P and Ŕ? E. magnitude of Ŕ? F. unit vector in the direction of R C. magnitude of P? D. unit vector in the direction of P? G. scalar product of P and R? H. vector product of P and R? 2. A stone is thrown from the top of a building upward at an angle of 30° with the horizontal with an initial speed of 20 m/s. The height of the building is 45.0 m. A. How long does it take the stone to reach the ground? and B. What is the speed of the stone just before it strikes the ground? 3. A wheel is under a constant angular deceleration of 5rad/s2. Its initial speed is 3rad/s. A. What angular distance in rad, rev and degrees will it travel just before coming to rest? B. How long will it travel just before coming to rest? 4. A block with mass m₁ = 6kg that slides on a table with μk = 0.2 is attached by a massless string over a massless, frictionless pulley to a hanging ball with mass…
- 180% P 7:35 stc ksa ll. Second H.W.pdf 1. Draw and label the vector with these components. Then determine the magnitude and angle of the vector. a- A, = 3 ,A, = -2 b- By = -2 ,B, = 2 2. What is the speed of horse in meter per second that runs a distance of 1.2 miles in 2.4 minutes? 3. A car moving along X- axis according on the function: X (t) = 2 t2 + 5 t + 7 on [1,2] Find: a- The average velocity. b- The acceleration at 3s. 4. Julie is walking around a track at a 2m/s for some exercise. She then decides to start jogging so she accelerates at a rate of 0.5m/s for 3 seconds. How far did Julie travel from the time she started to accelerate to the end of the 3 seconds? 5. Ralph uses a 2000 N force to push his car along a road for 1000 m. It takes him500 s to do this a- Calculate the amount of work that Ralph did on the car. b- Calculate the amount of power that he generated.1%Y. li. lin. A IY:10 : 2 Problems of chapt.. → Problems of chapter 2 and 3: 1. The polar coordinates of a point are r = 5.50 m and 0 = 240°. What are the cartesian coordinates of this point? 2. The driver of a car drives 3.00 km north, 2.00 km northeast (45.0° east of north). 4.00 km west, and then3.00 km southeast (45.0° east of south). Where does he end up relative to his starting point? Work out your answer graphically. Check by using components. 3. Vector A has x and y components of -8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and -6.60 cm, respectively. If A - B + 3C0, what are the components of C? 4. The vectors A and B are given by A = 2i +3j andB = -i+2j. (a) Determine the scalar product A.B. (b) Find the angle 0 between A and B. (c) Determine the vector product AXB. 5. The vector position of a particle varies in time according to the expression r = (3.00i - 6.00: 2 j) m. (a) Find expressions for the velocity and acceleration as functions of…Seatwork: Given points P (2,5. -1). Q (-1, -4,1). T (5.0.2). find the unit vectors a. the unit vectors Rra. Rar. and R b. the length of the perimeter of the triangle PQT c. the vector projection of Rra on R