For the two vectors in the figure below (from the textbook), A× B points B up down left right into the screen out of the screen A× B'is zero. A
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- For the vectors given in the following figure, use a graphical method to find the following resultants: (a) A+B , (b) C+B , (c) D+F , (d) AB , (e) DF , (f) A+2F , (g) C+2D ; and (h) A4D+2F .A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. Use the analytical method to determine the following: (a) Find his net displacement vector. (b) How far is the restaurant from the post office? (c) If he returns directly from the restaurant to the post office, what is his displacement vector on the return trip? (d) What Is his compass heading on the return trip? Assume the +x-axis is to the east.Suppose you add two vectors A and B . What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?
- Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, Indicate whether their velocity vectors are equal or otherwise. (a) Alice moves north at 6 knots and Bob moves west at 6 knots. (b) Alice moves west at 6 knots and Bob moves west a 3 knots. (C) Alice moves northeast at 6 knots and Bob moves south at 3 knots. (d) Alice moves northeast at 6 knots and Bob moves southwest a 6 knots. (e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.A physics student adds two displacement vectors with magnitudes of 8.0 km and 6.0 km. Which one of the following statements is true concerning the magnitude of the resultant displacement? O It must be 14.0 km. No conclusion can be reached without knowing the directions of the vectors. It must be 10.0 km. O It could have any value between 2.0 km and 14.0 km depending on how the vectors are oriented. O It could be equal to zero kilometers, depending how the vectors are oriented.A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle ?i above the horizontal as in the figure. If the initial speed of the stream is vi, at what height h does the water strike the building? (Use any variable or symbol stated above along with the following as necessary: g.)
- Consider two vectors C & D in XY-plane, shown in the figure beside. If C-D-12 m and a-30, the vector C (in m) is: -6 i+10.4j O 10 i+8.3j -10.4i +6j O5.5i+6.4j O 2.5i+ 8.6jWater leaves a fireman’s hose (held near the ground) with an initial velocity v0 = 11.5 m/s at an angle θ = 30.5° above horizontal. Assume the water acts as a projectile that moves without air resistance. Use a Cartesian coordinate system with the origin at the hose nozzle position, as shown. 1). Using v0, θ, and g, write an expression for the time, tmax, the water travels to reach its maximum vertical height. 2)Q1 B: Consider these two vectors A-2i+3j+5k and B=5i+3j+10k, find the following D=AXB a-D=11i+2j-15k b-D=5i+9j-11k c-D=3i-7j+5k d-D=15i+5j-9k
- The man at A wishes to throw two darts at the target at B so that theyarrive at the same time. If each dart is thrown with a speed of 12.0 m/s, determinethe angles θC and θD at which they should be thrown and the time between eachthrow. Note that the first dart must be thrown at θC (> θD), then the second dart isthrown at θDSuppose that the clock on our lecture room has a minute-hand length of 10 cm. (Use a coordinate system with the origin at center of clock and +x axis along the 3PM direction and the +y direction along the 12PM direction). From the 12 to 8 mark, for the tip of the minute hand: a) Sketch a vector diagram labeling ri, rf, Δr, Vi, Vf, and ΔV. b) Calculate the displacement vector in unit-vector notation. c) Calculate the average velocity vector in unit-vector notation. d) Calculate the average acceleration vector in unit-vector notation. e) Calculate magnitude and direction of the average acceleration vector. f) Calculate the magnitude and direction of the total acceleration of the tip of the minute hand at the 6 mark.From a tower of height yo a particle is projected vertically up with a velocity vo in free space (gravity free). The acceleration of particle at an instant is given as ā = k (v ×Ā), where v is instantaneous velocity vector and A is given as A = (-k), where y is the H y vertical coordinate of particle at that instant. (Take origin as foot of the tower) Answer the following questions. D 14. The speed of particle as a function of time will be (A) vo + kt (C) Vo-y/t 15. (B) vo+ (y/t)-(1/2)at (D) Vo The maximum height attain by the particle will be (A) y = Yo(1+evo/Kc) (C) y = Yo (1-evo/kc) (B) y = Yo(1+e */v) (D) y Yo (1-e-c/vo) t Yo (0, 0)
