VECTORS Important Questions from CBSE point of view LEVEL-1 1. Two forces have their resultant equal to either. At what angle are they inclined? 2. Add a velocity of 30 m/s eastwards to a velocity of 40 m/s northwards. Calculate the magnitude and direction of the resultant with the east. 3. Two forces whose magnitude are in the ratio 3 : 5 give a resultant of 28 N. If the angle of their inclination is 60, find the magnitude of each force. 4. An aeroplane takes off at an angle of 30 to the horizontal. If the component of its velocity along the horizontal is 250 km/h, what is its actual velocity? Find also the vertical component of velocity. 5. Determine the vector which when added to A= 3 i -5 j +7 k and B= 2i +4j -3k gives unit vector along y- direction. 6. Given A= 2i+3j+4k and B= 3i-5j+k. Find the angle between A and B. 7. What is the essential condition for the addition of two vectors? 8. What is the magnitude and direction of i+j? 9. Two forces 5 and 10 kg wt. are acting with an inclination of 120 between them. What is the angle which the resultant makes with 10 kg wt.? 10. Do A+B and A-B lie in the same plane? Explain. 11. Is the magnitude of A-B same as that of B-A?
12. The resultant of two equal forces acting at right angles to each other is 1414 N. Find the magnitude of each force. LEVEL 2 1. A man can swim at the rate of 5 km/h in still water. A river 1 km wide flows at the rate of 3 km/h. A swimmer wishes to cross river straight. a) Along what direction must he strike? b) What should be his resultant velocity? c) How much time he would take to cross? 2. A train is moving due east and a car is moving due north, both with same speed 30 km/h. What is the observed speed and direction of motion of car to the passenger in the train? 3. A person standing on the road has to hold his umbrella at 60 with the vertical to keep the rain away. He throws the umbrella and starts running at 20 m/s. He finds that rain drops are hitting vertically. Find the speed of the rain drops with respect to a) the road b) the moving person. 4. A ball is acted upon by following velocities. I) 3 m/s due east ii) 11 m/s due east iii) 5 2 due north east. Find the magnitude and direction of resultant velocity. 5. Given A+B+C+D=0, can the magnitude of A+B+C be equal to the magnitude of D? Explain. 6. Two vectors A and B are added. Prove that the magnitude and resultant vector cannot be greater than A+B and smaller than A-B or B-A.
7. There are two displacement vectors, one of magnitude 3 m and the other of magnitude 4 m. How would the two vectors be added so that the magnitude of the resultant vector be a) 7 metres b) 1 metre and c) 5 metres. 8. The position of a particle is given by r= 3.0 t I + 2.0t 2 j + 5.0 k where t is in seconds and the coefficients have the proper unit of r to be in metres. Find the velocity and acceleration of the particle in magnitude and direction at time t=3s. 9. A boat man can row with a speed of 10 km/h in still water. If the river flows steadily at 5 km/h, in which direction should the boat man row in order to reach a point on the other bank directly opposite to the point where he started? The width of river is 2 km. 10. A train is moving with a velocity of 30 km/h due east and a car is moving with a velocity of 40 km/h due north. What is the velocity of the car as appeared to the passenger in the train? 11. Find the length of A+B and A-B where A=3i+2j and B= i-2j+3k. 12. Given A= 4i 3j + k and B= -i + j +4k, find C such that A-B+C=0. 13. Find the angle between A and B where A= i+2j k and B= -i+j-2k. LEVEL 3 1. Find the values of T 1 and T 2 for the system shown in figure. Mass of block is 60 kg.
2. The sum of three vectors shown in figure is zero. Find the magnitude of other two vectors. 3. Rain is falling vertically with a speed of 35 m/s. A woman rides a bicycle with a speed of 12 m/s in east to West direction. What is the direction in which she should her umbrella? 4. Find the resultant force of the following forces which act upon a particle. a) 30 N due East b) 20 N due North c) 50 N due West d) 40 N due South 5. If A+B=C and A 2 +B 2 = C 2, show that A and B are mutually perpendicular. 6. In a harbor, wind is blowing at a speed of 72 km/h and the flag on the mast of the boat anchored on the harbor flutters along N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast? Answer- Towards East. 7. Find the angle between the force F= 3i+4j-5k and displacement s= 5i +4j +3k. Also find the projection of F on S. Answer - 71.3 and 16 N. 8. Can A X B and A.B be equal to zero at the same time?
PROJECTILE MOTION 1. Two tall buildings are 200 m apart. With what speed must a ball be thrown out of the window 540 m above the ground in one building, so that it will enter a window 50 m above the ground in the other? Ans: 20 m/s 2. A plane flying horizontally at 100 m/s at a height of 1000 m releases a bomb from it. Find a) time it takes to reach the ground b) the velocity with which the bomb hits the target in the ground 100/7 seconds, 172.1 m/s at an angle tan -1 (1.4). 3. A body is projected with a velocity of 40 m/s. After 2 seconds it crosses a vertical pole og height 20.4 m. Find the angle of projection and the horizontal range of projectile. (g=9.8 m/s 2 ). Ans- 141.4 m 4. Explain that a uniform circular motion is an accelerated motion. 5. A projectile can have same range R for two angles of projection. If t 1 and t 2 are times of flight in two cases, find the relation between horizontal range and two times of flight. Ans- t 1 t 2 =2R/g 6. A body of mass m is thrown with velocity v at an angle 30 to the horizontal and another body B of the same mass is thrown with velocity v at an angle of 60 to the horizontal, find the ratio of horizontal range and max height of A and B. 1:1 7. A projectile is given an initial velocity of i+2j where i is the unit vector in x-direction and j is the unit vector in y-direction. Find the Cartesian equation of its path. (g=10 m/s 2 ) Ans- y= 2x-5x 2.
8. A shot fired at a distance of 39.2 m from the foot of a pole 19.6 m high so that it just passes over it. Find the magnitude and direction of the velocity of the shot. Ans- 27.72 m/s ; 45. 9. A particle is projected with a velocity u so that its horizontal range is twice the greatest height attained. Find the horizontal range of it. (Ans- 4u 2 /5g)