PHYSICS. Relative velocity

Size: px

Start display at page:

Download "PHYSICS. Relative velocity"

Shanon Hill
5 years ago
Views:

1 AILY PRACTICE PROLEMS P4 Relative velocity Topics : Relative Velocity SECTION - I (Straight Objective Question) This section contains seven (7) multiple choice questions. Each question has four (4) options (a),, (c), (d) out of which ONLY ONE is correct.. A boat which rows with a speed of 5 kmh in still water crosses a river of width km along the shortest path in 5 min. The velocity of river water is (a) km h 3 km h (c) 4 km h (d) 5 km h - 9 R = resultant vel = 4km h = angle at which boat rows v sin tan u v cos cos u.u 5 R u v uv cos 4 u 5 u.u 6 = u + 5 u u = 9 u = 3 km h v 5 ms v = 5 4 km

2 . A train S, m long runs with a velocity 7 kmh ; while train T 3 m long is running in opposite direction with a velocity 8 kmh. The time taken by T to cross train S is (a) 5 sec sec (c) 5 sec (d) 5 sec (a) Velocity of S - train = ms Velocity of T - train = 3 ms Relative vel. of T w.r.t. s = 3 = 5 ms istance = l + l = 5 m time t 5 m 5 ms 5sec 3. A man swims in still water of a river of width with speed v. The river flows with velocity (v/). He swims making an angle with the upstream to cross the river in shortest distance. The time taken to cross the river is (a) /V vcos (c) vsin (d) v (c) v m = vel. of man = v v r = vel of river v v = v sin sin 3 time t v sin v v/ v m 4. A person aiming to reach the exactly opposite point on the bank of a strean is swimming with a speed of.5 ms at an angle of with teh direction of flow of the stream. The speed of the stream is (a) ms.5 ms (c).5 ms (d).433 ms (c) v = velocity of stream. Resultant of u and v must be R u =.5 ms, R = resultant velocity v = u sin ms river Relative Velocity

3 V u 3 R 5. A boat crosses a river from port A to port which are just on the opposite side. The speed of the water is V w and that of boat is V relative to still water. Assume V = V w. What is the time taken by the boat, if it has to cross the river directly on the A line (a) V 3 3 V (c) V (d) V (a) From figure, V sin V W Vw sin 3 V V V Time taken to cross the river, W t V cos V cos3 V 3 V V cos V sin Relative Velocity 3 A 6. A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of km. The minium time taken around a round trip is (a) 5 min 6 min (c) min (d) 3 min (d) For the round trip he should cross perpendicular to the river Time for trip to that side km.5hr To come back, again he take.5 hr to cross the river. Total time is 3 min, he 4 km / hr goes to the other bank and come back at the same point. 7. Consider a collection of large number of particles each with speed v. The direction of velocity is randomly distributed in the collection. The magnitude of relative velocity between a pair of collection particles averaged over all the particles is (a) zero greater than v (c) less than v (d) v V W

4 Consider two particles with angle between their directions of velocities then V = V V. Hence magnitude of relative velocity V V V V V cos V V sin. V V V and average value of V r is or Vr. d V Vr sin sin V d d V V 4V cos cos8 cos SECTION-II (One or More than correct objective Question) This section contains three (3) multiple choice questions. Each question has four (4) options (a),, (c), (d) out of which ONE OR MORE is/are correct. 8. A river flows at ms. The man can swim in still water with velocity of 4 ms. The angle at which man must swim with the banks so that he crosses the river in the shortest distance is (a) 3 up stream 3 down stream (c) 6 up stream (d) 6 down stream (d) 4 sin Sin 3 angle with downstream = (9 ) = 6 with downstream ms V. 4 ms River O ms 9. A boat crosses the river in short possible route. The speed of the boat in still water is 3 ms. The average speed of the boat while crossing the river comes out to be ms. The velocity of the river is (a) 5 ms 5 ms (c) ms (d) 4 ms (a) V b = velocity of boat = 3 ms V a = average speed = ms V r = velocity of river = 5 ms 3 4 Relative Velocity

5 . River is flowing with a velocity v 4iˆ m/s. A boat is moving with a volocity of v (4)() 5 m/s R relative to river. The width of the river is m along y-direction. Choose the correct alternative(s). (a) The boatman will cross the river in 5 s. Absolute velocity of boat man is 5 m/s. (c) rift of the boatman along current is 5 m (d) The boatman can never cross the river. (a, b, c) Absolute velocity of boatman is v v v v R R = ( iˆ 4)(4) ˆj iˆ = iˆ 4 ˆj 4 j V Time t = 5 s 4 rift x = () (5) = 5 m i v (4)() 5 m/s SECTION - III (Assertion & Reasoning Type Question) This section contains three (3) assertion & reasoning type questions. Each question has four (4) options (a),, (c), (d) out of which ONLY ONE is correct. Statement based Questions : For the following question, choose the correct answer from the codes (a),, (c) and (d) defined as follows ; (a) Statement I is true, Statement II is true; Statement II is correct explanation for Statement I. Statement I is true, Statement I is true; Statement II is not correct explanation of Statement I (c) Statement I is true; Statement II is false. (d) Statement I is false; statement II is true.. STATEMENT- For an observer looking out through the windows of a fast moving train, the near by objects appear to move in opposite direction to the train. While distant appear to be stationary STATEMENT- If the observer and the object are moving with velocities V and V respectively with reference to a laboratory frame the velocities of the object with respect to the observer is V V oth statements are true but reason is not correct explanation of assertion. istant objects motion depends on the agle subtended at eye. It is illustrated in fig. O Relative Velocity 5

6 . STATEMENT The relative velocity between any two bodies moving in opposite direction is equal to the sum of the velocities of two bodies.() STATEMENT Some times relative velocity between two bodies is equal to the difference in velocities of the two bodies. When two bodies are moving in opposite direction relative velocity between then is equal to sum of the velocities of bodies (V = V (V ) =V + V ). ut if the bodies are moving in the same direction their relative velocity is equal to difference in velocities of bodies (V r = V V ). 3. STATEMENT A body, what ever its motion, is always at rest in a frame of reference which is fixed to the body itself. STATEMENT The releative velocity of a body with respect to itself is zero. (a) A body has no relative motion with respect to itself. Hence in frame of reference attached to body itself its velocity is zero. SECTION - IV (Passage ased Question) This section contains one () paragraph based upon the paragraph three(3) multiple choice questions have to be answered. Each question has four(4) options (a),, (c), (d) out of which ONLY ONE is correct. Two parallel rail tracks run north south. Train A moves north with a speed of 54 km/h and train moves south with a speed of 9 km/ h. 4. The relative velocity of with respect to A is (a) 9 km/h 44 km/h (c) 3 km/h (d) none of these Let v A = 54 km/h then v = 9 km/h S ( ) N (+) 54 km/h 9 km/h Relative velocity of with respect to A v A 9 54 = 44 km/h The velocity of train with respect to train A appears 44 km/h along south. 5. The relative velocity of ground with respect to is (a) 9 km/h 44 km/h (c) 7 km/h (d) 6 km/h (a) Relative velocity of ground with respect to train = v ground v = 9 = 9 km/h To train, the ground appears to move with a speed of 9 km/h along south. 6. The velocity of a monkey running on the roof of the train A against its motion (with a velocity of 8 km/ h with respect to the train A) as observed by a man standing on the ground is (a) 33 km/h 36 km/h (c) 99 km/h (d) zero 6 Relative Velocity

7 The velocity of monkey with respect to train A [v monkey ] train A = [v monkey ] ground [v train A ] ground or [v monkey ] ground = [v monkey ] train A + [ v train A ] ground = 36 km/h. SECTION - V (Matrix Match Type) This section contains one () question. It contains statements given in two columns, which have to be matched. Statements in column I are labelled as A,, C and whereas statements in column II are labelled as p, q, r and s. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A p, r ; q, s; C r and q, then the correctly bubbled matrix will look like the following: 7. Match the following columns. Column I p q r s p q r s p p p q q q r r r s s s Fig. 3.4 Relative Velocity 7 A C Column II (a) It is raining verticaly at 3 m s. If wind blows horizontally at m s,. The apparent velocity of rainfall is (p) m s A boat is moving at m s towards north and another boat is moving at m s towards north-west. Find the relative velocity of the second boat with respect to the first is equal to (q) 5 m s (c) From the top of a tower, two particles are dropped at an interval of s. Find the relative velocity and relative acceleration of the particles during the fall. Acceleration due to gravity = m s. (r) 4 m s (d) A police jeep is chasing with velocity of.5 m s a thief in another jeep moving with velocity 4.5 m s. Police fires a bullet with muzzle velocity of 8 m s. The velocity with which it will strike the car of the thief is (s) m s (a) (r) ; (s) ; (c) (p) ; (d) (q) (d) Effective speed of the bullet = speed of bullet + speed of police jeep = 8 m s +.5 m s = (8 +.5) m s = 9.5 m s speed of thief's jeep = 4.5 m s Velocity of bullet w.r.t thief's car = = 5 m s SECTION - VI (Integer Type) This section contains three (3) questions. The answer to each of the question is a single digit integer, ranging from to Velocity of a boat in still water is 5 km h. The boat takes 5 min to cross a river of width km perpendicularly. The velocity of current is The boat crosses a river of width km in 5 min or in. 4 h The resultant of the velocity of the boat and current is w (say) and u v w u w 4 km h / 4

8 Let the velocity of the boat in still water be v and the velocity of current be u. From Fig v = u + w or, u = v + w or, u v w km. h. 9. It is raining vertically at 3 m. s. If wind blows horizontally at m. s, what will be the apparent velocity and direction of rainfall? V R = 3.ms V W = ms Let the resualt velocity be R R m / s irection of wind y V w O V w x x R V R. A boat is moving at 5 km. h towards north and another boat is moving at 5 km. h towards north-west. Find the relative velocity of the second boat with respect to the first. Required relative velocity of the second boat w.r. to the first boat is R N 5 km / h y 5 km/h 5 km/h V w W R O E 3 km/h R 5 5 R R 5 S 8 Relative Velocity

Q1. In a circular track (distance 400 m) an athlete runs 1/4 the of the ground. So what would be the displacement?

Class: 9 Subject: Physics Topic: Motion in a straight line No. of Questions: 20 Q1. In a circular track (distance 400 m) an athlete runs 1/4 the of the ground. So what would be the displacement? Given,