Unit-1. 10th grade. Elective Fizx. v cm =v c - v m. v cm =5 3 m/s. Force & Motion. Solutions 1.2 Relative Motion page v c. -v m. 5 m/s.

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1 page - 23 N W 5 m/s 60 o v c 5 m/s E -v m S 5 3 m/s v cm =v c - v m v cm =5 3 m/s

2 page - 23 N v c W 60 o 60 o -v ct E S -v t v ct =v c - v t v ct =10 m/s (due east)

3 page Cars A, B, C, and D move toward an intersection at equal speeds. When two vectors that have the same magnitude are added, their magnitude increases as the angle between them decreases. The angle between -v A and v C is the smallest then v CA is the greatest. Which car is the fastest with respect to the driver of the car A?

4 page - 23 N v tc 10 m/s 6 m/s W 37 v o c E 8 m/s 8 m/s S v tc =v t - v c v t =v c + v tc v t =6 m/s due north

5 page - 24 v T -v X v TX The driver of car X observes car T as it is moving due south.

6 page - 24 v K v KM -v M -v M v L v LM

7 page Cars K, L and M are moving in the same direction with constant velocities. The driver of car K sees car L as moving toward east and the driver of car L sees car M as moving toward east. If the driver of car K sees car L as moving due east then its speed must be smaller than the speed of L. If the driver of car L sees car M as moving due east then its speed must be smaller than the speed of M. Which of the following relations between the speeds of the cars is/are possibly correct? I. v K > v L II. v L > v M III. v M > v K v M > v L > v K Statements I and II are wrong and III is correct.

8 page Two skiers, K and L, are moving at constant speeds of 9 m/s and 12 m/s respectively as shown in the figure. W N 12 m/s 37 o 53 o -v L E 9 m/s v K S v KL =v K - v L What is the velocity of skier K with respect to skier L? v KL =15 m/s due east

9 9. The velocity of the river is constant and it is in west-east direction. Three swimmers A, B and C start to swim from point O at constant velocities v A, v B and v C with respect to river. Swimmer B reaches at point M at the opposite riverbank. page - 25 v r Answer the following questions. a) Swimmer A reaches at point at the opposite riverbank. b) Swimmer C reaches at point at the opposite riverbank. c) Compare the times of swimmers to reach the opposite riverbank. d) Compare the velocities of swimmers with respect to the ground. a) K b) S c) The vertical components of B and C are equal and that of A is smaller. So, the times of them to reach opposite riverbank is related as A>B=C d) B=C>A (see the orange arrows in the figure.)

10 page The velocity of the river is constant and it is in west-east direction. A swimmer starts to swim from point O directly towards point A at a velocity of v s with respect to river and it reaches at point B at the opposite riverbank. The horizontal displacement of the swimmer is x, the time to reach the opposite riverbank is t and the velocity of the swimmer with respect to ground is v. v r v v r x v B / How would x, t and v change if the velocity of the river were greater? x :. t :. v :. When v r increases, x and v increase. v s is the same than t will be the same. Time depends on the vertical component.

11 page A swimmer swims from point A to point B in 8 seconds and returns to point A in 20 seconds. From A to B; 80 = (v s +v r ).8 From B to A; 80 = (v s -v r ).20 Calculate the velocity of the river and velocity of the swimmer with respect to the river in m/s. + v s +v r =10 v s -v r =4 v s =7 m/s v r =3 m/s

12 page Two swimmers A and B encounter the stream from point K as in the figure. The velocity of the river is 4 m/s. For A v Ax = 10.cos37 o =10.0,8=8 m/s v Ay = 10.sin37 o =10.0,6=6 m/s t = (120)/6=20 s X A = (8-4).20=80 m (left) What will be the horizontal distance between them when they reach to opposite riverbank? For B t = (120)/6=20 s X B = (4).20=80 m (right) The distance between them is 160 m as they reach the opposite riverbank.

13 page A swimmer starts to swim from point O and reaches at the opposite riverbank at point M. v x = 5.cos37 o =5.0,8=4 m/s v y = 5.sin37 o =5.0,6=3 m/s t = (60)/(3)=20 s If the width of the river is 60 m, calculate the velocity of the river with respect to the ground. X=(v r +4).t 90=(v r +4).20 v r = 0,5 m/s

14 page The width of the river is 40 m. The speed of the river is constant and it flows through east-west direction. A swimmer starts to swim from point O and heads towards point K but it reaches point L in 5 seconds. The distance between points K and L is 30 m. X=v r. t 30=v r.5 v r = 6 m/s d=v. t 40=v.5 v = 8 m/s What is the speed of the swimmer with respect to ground in m/s? v r (wrt ground)= 10 m/s

15 page Velocities of four boats with respect to river and the velocity of the river are given in the figure. Boats start their motion at the same time. A B Which of the two boats can meet at the river? (The figure is scaled.) At point A, K & L at point B, K & N meet.

16 page Two swimmers X and Y swim toward each other in a river as shown in the figure. The velocity of the river is v r. The velocity of swimmer X with respect to river is v x and the velocity of swimmer Y is v y. x is the distance covered by swimmer X. For X; d=(2v+v).t then d=3vt For Y; 8x-d=(2v-v).t then 8x-d=vt At which point do the swimmers meet? (Figure is scaled.) 8x-3vt=vt then vt=2x 8x-d=2x then d=6x They will meet at point G.