RESULTANT VECTOR QUESTIONS

1.Two forces act at a point in directions inclined to each other at 120°. If the bigger force is 5 Nand their resultant is at right angles to the smaller force, find the resultant and the smaller force

2.An aeroplane takes off at an angle of 45⁰ to the horizontal. If the vertical component of its velocity is 300 kmph, calculate its actual velocity. What is the horizontal component of velocity?

3.A force is inclined at 60o to the horizontal . If the horizontal component of force is 40 N, calculate the vertical component.

4.A body is projected upwards with a velocity of 30 m s-1 at an angle of 30° with the horizontal. Determine (a) the time of flight (b) the range of the body and (c) the maximum height attained by the body.

5.The horizontal range of a projectile is 4√3 times its maximum height. Find the angle of projection. 2.49 A body is projected at such an angle that the horizontal range is 3 times the greatest height . Find the angle of projection

6.Two forces of magnitude 12 N and 8 N are acting at a point. If the angle between the two forces is 60°, determine the magnitude of the resultant force?

7.The sum of two forces inclined to each other at an angle is 18 kg wt and their resultant which is perpendicular to the smaller force is 12 kg wt Find the forces and the angle between them.

8.The following forces act at a point (i) 20 N inclined at 30o towards North of East (ii) 25 N towards North (iii) 30 N inclined at 45o towards North of West (iv) 35 N inclined at 40o towards South of West. Find the magnitude and direction of the resultant force.

9.Find the magnitude of the two forces such that it they are at right angles, their resultant is 10 N. But if they act at 60o, their resultant is 13 N.

10.The Cartesian coordinates of a point in the xy plane are (x, y) = (3.50, 2.50) m as shown in Figure 3.3. Find the

polar coordinates of this point.Write it as the position vector and find the direction of r

11.A car travels 20.0 km due north and then 35.0 km in a direction 60.0° west of north as shown in Figure. Find the magnitude and direction of the car’s resultant displacement.

12Find the sum of two displacement vectors Aand B lying in the xy plane and given by A =(2.0 i^ + 2.0 j^)  m and B=(2.0 i^- 4.0 j^)  m

VECTOR POSITION , DISSPLACEMENT,UNIT VECTORS QUESTIONS

1. Write an example of zero vector.

2. State the essential condition for the addition of vectors.

3. When is the magnitude of (A + B) equal to the magnitude of (A − B)?

4. What is the maximum number of component into which a vector can be resolved?

5. Does a vector quantity depends upon frame of reference chosen ?

6. What is the unit vector perpendicular to the plane of vectors A and B ?

7. What is the angle between (A + B) and (A × B)?

8. Two vectors A & B are inclined to each other at an angle θ . Using Parallelogram law of vectors addition, find the magnitude and direction of their resultant.

9. When the angle between two vectors of equal magnitudes is 2π / 3, prove that the magnitude of the resultant is equal to either.

10. If A = 3ˆi + 4ˆj and B = 7ˆi + 24ˆj, find a vector having the same magnitude  as B and parallel to A

11. (a) If ˆi and ˆj are unit vectors along x & y axis respectively then what is magnitude and  direction  of (ˆi + ˆj) and (ˆi − ˆj) ? (b) Find the components of vector a= 2ˆi + 3ˆj along the directors of vectors (ˆi + ˆj) and (ˆi − ˆj) .

12. A motorboat is racing towards north at 25 kmh–1 and the water current in that region is 10 kmh-1 in the direction of 60° east of south. Find the resultant velocity of the boat.

13. An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a

        ground observation point by the aircraft position 10 second apart is 30°, what is the 

        speedof the   aircraft?

14. A boat is moving with a velocity (3ˆi − 4ˆj) with respect to ground. The water in river is

         flowing    with a velocity (−3ˆi − 4ˆj) with respect to ground. What is the relative 

         velocity ofboat with   respect to river?

15. If the magnitude of two vectors are 3 and 4 and their scalar product is 6, find angle between them.

16. Find the value of λ so that the vector A = 2ˆi + λˆj + Kˆ and B = 4ˆi − 2ˆj + 2Kˆ are perpendicular to each other.

17. (a) What is the sum in unit–vector notation of the two vectors a = 4.0i + 3.0j and b = −13.0i + 7.0j? (b) What are the magnitude and direction of a + b?

18.  Vector a has magnitude 5.0 m and is directed east. Vector b has magnitude 4.0 m and is directed 35◦ west of north. What are (a) the magnitude and (b) the direction of a + b? What are (c) the magnitude and (d) the direction of b − a? Draw a vector diagram for each combination.

19. If a − b = 2c, a + b = 4c and c = 3i + 4j, then what are a and b?

Two equal forces are acting at a point with an angle of 60° between them. If the resultant force is equal to 20√3 N, find the magnitude of each force