NTSEUseful math:

Ex.

Ans.

Vectors:

Contents-

Exercise:

1. Find the resultant of two forces acting on a body- a) 40 N , vertically upwardsb) 30 N , horizontally

2. Find the vertical and horizontal component of force of 100 N directed at 30° above the horizontal.

3. A woman pushes a lawnmower at 60° with vertical. How much force she exerts normal to the ground? 51.4N

4. An airplane is heading northeast at a velocity of 550 kmph. What are its northward and eastward components of velocity? 389 kmph

5. A boat heads northwest at 20 kmph in river that flows east at 6 kmph. Find magnitude and direction of boat’s velocity relative to surface of earth. 16.3kmph@WofN

6. An airplane whose velocity is 120 kmph just takes off from runway. A car driving at 100 kmph on runway sustains just below the airplane. At what angle is the airplane climbing? 34°

7. A boat moving at 36 kmph crossing a river in which water current is at 12kmph. In what direction should the boat head to reach on other side of river just in front of the starting point? 19° upstream of directly across the river

Motion in one dimension:

Contents-

Exercise:

1. You are standing 100m north of your car when an alligator appears 20m north of you and begins to run towards you at 8m/s. At the same moment you start to run towards your car at 5m/s-a) Will you reach the car before the alligator takes over you?b) If not, how far from your car does the alligator have lunch of you?

2. A car travels at 100kmph for 2 hr and at 60 kmph for next 2 hr towards east and then at 80 kmph finally for 1 hr towards west. Find the average speed and average velocity of car.

3. An airplane at speed of 500kmph covers a distance of 1000 km in 2.5 hr. How strong is the headwind against it?

4. How long does it take an echo to return a woman standing at 300m from a cliff. Sound speed in air is 343 m/s.

5. A car moving at 100kmph is 80 km behind another car moving at 60 kmph in same direction. How far does the first car travel before it overtakes second car?