1. If one of the rectangular components of a force of 100 N is 50 N, find the other component.
2. Two bodies A and B are attached to the ends of a string passing over a frictionless pulley such that the masses hang vertically. If the mass of one body is 96kg, find the mass of second body, which moves downward with an acceleration of 0.2 m/s2 and the tension in the string. (g = 9.8 m/s2)
3. An artillery cannon is pointed upward at an angle 35° with respect of horizontal and fires a projectile with an initial velocity of 200m/s. If the air resistance is negligible, find the maximum height reached by the projectile and the range of the projectile.
4. Two vectors have magnitudes 4 and 5 units. The angle between them is 30°. Taking the first vector along x-axis, calculate the magnitude and the direction of the resultant.
5. Given that , find , , and the angle between.
6. A 100 gm bullet is fired into a 12kg block which is suspended by a long cord. If the bullet is embedded in the block and the block and the block rises by 5cm. What was the speed of the bullet?
7. The radius of the moon is 27% of the earth’s radius and its mass is 1.2% of the earth’s mass. Find the acceleration due to gravity on the surface of the moon. How much does a 980 N body weigh there.
8. Find the value of P for which the following vectors are perpendicular to each other.
9. A boy throws a ball vertically upward with a speed of 25m/s. On the way down, it is caught at a point 5m above the ground. How fast was it coming down at this point? How long did the trip take?
10. A string 1m long would break when its tension is 69.6N. Find the greatest speed at which a ball of mass 2kg can be whirled with the string in a vertical circle.
11. A ladder rests against a smooth wall at an angle of 60° with the ground. The ladder weighs 200 N and its centre of gravity is at one thirds of its length from the base. Determine the frictional force, which prevents the ladder from slipping, and the coefficient of static friction.
12. If two vectors are such that A = 3 and B = 2 and = 4, evaluate and .
13. If find a unit vector parallel to .
14. A mortar shell is fired at ground level target 490m away with an initial velocity of 98m/s. Find the two possible values of the launch angle. Calculate the minimum time to hit the target.
15. Find how deep from the surface of earth a point where earth a point is where the acceleration due to gravity is half the value on the earth’s surface.
16. Given . Find the magnitude of vectors , and .
17. A minibus starts moving from the position of rest at a bust stop with a uniform acceleration during the 10th minute of its motion it covers a distance of 95m. Calculate its acceleration and the total distance it covers in 10 minutes.
18. Calculate the work done by a force given by in displacing a body from the position A to the position B. The position vectors A and B are