Topic : One dimensional motion.

Q.1) A driver having a definite reaction time, is capable of stopping his car over a distance of 30 m on seeing a red traffic signal, when the speed of the car is 72 km/hr and over a distance of 10 m when the speed is 36 km/hr. Find the distance over which he can stop the car if it were running at a speed of 54 km/hr. Assume that his reaction time and the deceleration of the car remains same in all the three cases.

Q.2) A driver takes 0.2 sec to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of 54 km/hr and the brakes cause a deceleration of 6 m/s², find the distance traveled by the car after he sees the need to put the brakes on.

Q.3) A ball is dropped from a balloon going up at a speed of 7m/s. If the balloon was at a height 60 m at the time of dropping the ball , how long will the ball take in reaching the ground ?

Q.4) A person sitting on the top of a tall building is dropping balls at regular intervals of one second. Find the position of 3rd, 4th and 5th ball when the 6th ball is being projected.

 Q.5) A particle starting from rest and moving with uniform acceleration 0.3 m/s² describes in the last second of its motion 9/25 th of the whole displacement. How long has it been in motion and what is the whole displacement traveled ?

Q.6)A particle moving with uniform acceleration in a straight line traverses 3 m in the 8th second and 5 m in the 16th second of its motion. What is the average velocity of the particle for the journey from the beginning of the 8th second to the beginning of the 17th second ?

Q.7) The driver of an express train moving at 90 km/hr sights a fright train 170 m ahead of him on the same track moving in the same direction and puts on the breaks to get a deceleration of 0.75 m/s². At the same instant, the driver of the fright train which is moving at 18 km/hr apprehending danger from behind makes his train pick up an acceleration of 0.45 m/s². Determine whether a collision can be averted ?

Q.8) From the edge of a cliff 196 m high a stone A is projected vertically upward with a velocity of 29.4 m/sec. four seconds after A is projected another stone B is dropped from the same point. Find when & where A will overtake B.

Q.9) Water drops from the nozzle of a shower onto the floor 3.24 m below. The drops fall at regular intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall. Find the location of the drops when a drop strikes the floor.

Q.10)The speed of a train increases at a constant rate a from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate b .If l is the total distance described, prove that the total time taken is[( 1/v)+{(v/2)[(1/a)+(1/ b)]}]

Q.11)An elevator is descending with uniform acceleration. To measure the acceleration, a person in the elevator drops a coin at the moment the elevator starts. The coin is 6 ft above the floor of the elevator at the time it is dropped. The person observes that the coin strikes the floor in 1 second. Calculate from these data the acceleration of the elevator.

Q.12) A staircase contains three steps each 10 cm high and 20 cm wide. What should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane ?

Q.13) A person is standing on a truck moving with a constant velocity of 14.7 m/sec on a horizontal road. The man throws a ball in such a way that it returns to the truck after the truck has moved 58.8 m. find the speed and the angle of projection (a) as seen from the truck, (b) as seen from the road.

Q.14) A train starts from rest and moves with a constant acceleration of 2 m/s² for half a minute. The brakes are then applied and the train comes to rest in one minute. Find (a) the total distance moved by the train, (b) the maximum speed attained by the train and (c) the position(s) of the train at half the maximum speed.

Q.15) A healthy young man standing at a distance of 7 m from a 11.8 m high building sees a kid slipping from the top floor. With what speed (assumed uniform) should he run to catch the kid at the arms height (1.8m) ?

Q.16) An NCC parade is going at a uniform speed of 6 km/hr through a place under a berry tree on which a bird is sitting at a height of 12.1 m. At a particular instant the bird drops a berry. Which cadet (give the distance from the tree at the instant) will receive the berry on his uniform.

Q.17) A ball is dropped from a height. if it takes 0.2 sec to cross the last 6 m before hitting the ground, find the from which it was dropped. Take g = 10 m/s².

Q.18) A 11.7 ft wide ditch has approach roads with at an angle of 15⁰ with the horizontal. With what minimum speed should a motorbike be moving of the road so that it safely crosses the ditch?

Q.19) A car decelerates from rest at a constant rate a for some time , after which it decelerates at a constant rate b to come to rest. If the total time lapse is "t" seconds. Calculate:
(i) the maximum velocity reached (ii) the total distance traveled.

Ans: Topic : One dimensional motion.

Q.1) 0.5 s, -10m/s² , 18.75 m. Q.2) 22 m Q.3) 4.3 sec Q.4) 44.1 m, 19.6 m and 4.9 m below the top Q.5) 5 sec, 3.75 m Q.6)4 m /sec Q.8) 8 sec after A , 78.4 m below edge. Q.9)0.36 m, 1.44 m below shower. Q.11) 20 ft/sec² Q.12) 2 m/sec Q.13) (a) 19.6 m/sec (upward) (b) 24.5 m/sec at 53⁰ with horizontal. Q.14) (a) 2.7 km (b) 60 m/sec (c) 225 m and 2.25 km Q.15) 4.9 m/sec. Q.16) 2.62 m. Q.17) 48 m. Q.18) 32 ft. Q.19) [(ab)/(a+b)]t ;{(1/2)[(ab)/(a+b)]} t².

Topic: Two & Three dimensional motion

Projectile and circular motion.

Q.1) A shell bursts on contact with ground and the pieces from it fly off in all directions with all speeds unto 30 ms^-1. Show that a man standing 30 m away is in danger for nearly 5 seconds.

Q.2) The range of a rifle bullet is 1000m, when q is the angle of projection. If the bullet is fired with the same angle from a car traveling horizontal at 36 km/hr towards the target , show that the range will be increased by . (1000/7)Ötanq m

Q.3) A bomber ,flying upward at an angle of 53⁰ with the vertical , releases a bomb at an altitude of 800 m. The bomb strikes the ground 20 s after its release. Find
(i) the velocity of the bomber at the time of release of the bomb.
(ii) the maximum height attained by the bomb.
(iii) the horizontal distance traveled by the bomb before it strikes the ground.
(iv) the velocity (magnitude and direction) of the bomb just when it strikes the ground. [ sin53⁰ = 0.8 , cos53⁰ = 0.6 , g = 10 ms^-1 ]

Q.4) Two shots are fired simultaneously from the top and bottom of a vertical tower AB at angles b and g with horizontal respectively. Both shots strikes at the same point C on the ground at distance 's' from the foot of the tower at the same time. Show that the height of the tower is s( tang - tanb ).

Q.5) A heavy particle is projected form a point at the foot of a fixed plane, inclined at an angle 45⁰ to the horizontal, in the vertical plane containing the line of greatest slope through the point if f (> 45⁰) is the inclination to the horizontal of the initial direction of projection, for what value of tanf will the particle the plane (I) horizontally(ii)at right angle.

Q.6) Two masses m₁ = 4 kg and m₂ = 1 kg are attached to each other and to a pivot by strings. The distance of the masses from the pivot are r₁ = 2 m and r₂ = 4 m. The speed of m₁ is 5 ms^-1.
(i) Find the tension T₁ and T₂ in the strings, if the masses rotate on a horizontal frictionless plane keeping the strings taut along a radial line.
(ii) If the masses are made to rotate in vertical plane, find the tension T₁ in the string when m₁ and m₂ are vertically below the pivot.

Q.7) A stone is thrown horizontally with a speed 10 ms^-1. Find the radius of curvature its trajectory at the end of 3 seconds after the motion began. Disregard the resistance of air. ( g = 9.81 ms^-1 ).

Q.8) A hemispherical bowl of radius = 0.1 m is rotating about its own axis ( which is vertical), with an angular velocity w . A particle of mass 10^-2 kg on the frictionless inner surface of the bowl is also rotating with the same w . The particle is at a height h from the bottom of the bowl.
(i) Obtain the relation between h and w . What is the minimum value of w needed, in order to have a non-zero value of h ?
(ii) It is desired to measure g using this setup, by measuring h accurately. Assuming that R and h are known precisely, and that the least count in the measurement of h is 10^-4 m, what is the minimum possible error D g in the measured value of g ?

Q.9) A smooth circular tube is kept ins a vertical plane. A small sphere can slide freely inside the tube is placed at its highest position in the tube. If the sphere is slightly displaced from its position of rest show that the force exerted by the sphere on the walls of the tube is mg(3 cosq - 2) where m is the mass of the sphere and q is its angular displacement from the highest position.

Q.10)A horizontal plane supports a stationary vertical cylinder of radius R and disc A attached to the cylinder by a horizontal thread AB of length l₀. An initial velocity v₀ is imparted to the disc as shown. How long will it move along plane until it strikes against the cylinder? The friction is assumed to be constant.

ANS:- 

Q.3) (i) 100 ms^-1 (ii) 980 m (iii) 1600 m (iv)161.2 ms^-1 ; 60⁰15'
Q.5) (i) tanf = 2 (ii) tanf =3.
Q.6) (i) T₁ = 75N , T₂ = 25 N. ; (ii) T₁ = 125 N, T₂ = 35 N.
Q.7) R = 306.08 m.
Q.8) (i) w = 7Ö 2 rad s^-1 (ii) D g = 98 x 10^-4 ms^-2.
Q.10)  [(l₀² )/(2Rv₀)]