Syllabus: Scalar and vector quantities; position and displacement vectors, general vectors and their notations; equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors, Unit vector; resolution of a vector in a plane, rectangular components, Scalar and Vector product of vectors. Motion in a plane, cases of uniform velocity and uniform acceleration-projectile motion, uniform circular motion.
Equations of motion for plane ppt
Numericals:
13. Calculate the angular speed of second’s hand of a clock. If the length of second’s hand is 2cm, calculate speed of its tip. Answer: (π/15 cm/s).
12. A particle moves in a circle of radius 20 cm with 120 rev/min. find centripetal acceleration. Answer: 320π2 cm/s2.11. A body is projected such that its KE at top is 3/4th of its initial KE. What is the initial angle of projection? 300.
10. A particle is projected at an angle of 450 with a velocity of 9.8 m/s. what will be its horizontal range? ans 9.8 m.
9. The max. range of a projectile is 2/√3 times its actual range. What is the angle of projection for the actual range? Answer: 600 or 300
8. The equation of trajectory of an oblique projectile is y = √3.x - gx2/2. What is the initial velocity and angle of projection? Answer: 2 m/s, 600
7. A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with an initial speed of 15 m/s. neglecting air resistance, find the time taken by the stone to reach the ground, and the speed with which it hits the ground. ( Use g=9.8 m/s2 )
6. A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600m/s to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? ( Use g=10 m/s2 )
5. A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies breaks and reduces his speed at the constant rate of 0.5 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn? NCERT
4. A ship moves due east at 12 km/h for 1 h and then turns exactly towards south to move for an hour at 5 km/h. calculate its average velocity for the given motion. Ans 6.5 km/h
3. A ball is thrown vertically up. It has a speed 10m/s, when it has reached ½ the maximum height. How high does the ball rise? g = 10 m/s2. Answer: 10 m.
2. Find unit vector along 4i + 6j.
1. If A= 3i + 4j and B= 7i + 24j, find a vector having same magnitude as B and parallel to A. Ans 15i + 20j
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