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PART - I : OBJECTIVE QUESTIONS Single choice type 1. A bomber plane moving at a horizontal speed of 20 m/s releases a bomb at a height of 80 m above ground as shown. At the same instant a Hunter of negligible height starts running from a point below it, to catch the bomb with speed 10 m/s. After two seconds he realized that he cannot make it, he stops running and immediately holds his gun and fires in such direction so that just before bomb hits the ground, bullet will hit it. What should be the firing speed of bullet. (Take g = 10 m/s2) 10 m/s Ground (A) 10 m/s (B) 20 m/s (C) 10 m/s (D) None of these 2. A particle is projected from a point (0, 1) on Y-axis (assume + Y direction vertically upwards) aiming towards a point (4, 9). It fell on ground on x axis in 1 sec. Taking g = 10 m/s2 and all coordinate in metres. Find the X-coordinate where it fell. (A) (3, 0) (B) (4, 0) (C) (2, 0) (D) ( 2 , 0) 3. Three stones A, B, C are projected from surface of very long inclined plane with equal speeds and different angles of projection as shown in figure. The incline makes an angle with horizontal. If HA, HB and HC are maximum height attained by A, B and C respectively above inclined plane then : (Neglect air friction) (A) H + H = H (B) H2 H2 H2 A C B A C B (C) H + H = 2H (D) H2 H2 2H2 A C B A C B 4. A ball is thrown from bottom of an incline plane at an angle from the inclined surface up the plane. Another ball is thrown from a point on the inclined plane with same speed and at same angle from the inclined surface down the plane. If in the two cases, maximum height attained by the balls with respect to the inclined surface during projectile motion are h1 and h2 then : (A) h1 > h2 (B) h1 < h2 (C) h1 = h2 (D) All the three can be possible 5. A particle is projected from surface of the inclined plane with speed u and at an angle with the horizontal. After some time the particle collides elastically with the smooth fixed inclined plane for the first time and subsequently moves in vertical direction. Starting from projection, find the time taken by the particle to reach maximum height. (Neglect time of collision). 2u cos (A) g u (sin cos) (C) g 2u sin (B) g 2u (D) g 6. Two stones A and B are projected from an inclined plane such that A has range up the incline and B has range down the incline. For range of both stones on the incline to be equal in magnitude, pick up the correct condition. (Neglect air friction) (A) Component of initial velocity of both stones along the incline should be equal and also component of initial velocity of both stones perpendicular to the incline should be equal. (B) Horizontal component of initial velocity of both stones should be equal and also vertical component of initial velocity of both stones should be equal. (C) Component of initial velocity of both stones perpendicular to the incline should be equal and also horizontal component of initial velocity of bo

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PART - I : OBJECTIVE QUESTIONS Single choice type 1. A bomber plane moving at a horizontal speed of 20 m/s releases a bomb at a height of 80 m above ground as shown. At the same instant a Hunter of negligible height starts running from a point below it, to catch the bomb with speed 10 m/s. After two seconds he realized that he cannot make it, he stops running and immediately holds his gun and fires in such direction so that just before bomb hits the ground, bullet will hit it. What should be the firing speed of bullet. (Take g = 10 m/s2) 10 m/s Ground (A) 10 m/s (B) 20 m/s (C) 10 m/s (D) None of these 2. A particle is projected from a point (0, 1) on Y-axis (assume + Y direction vertically upwards) aiming towards a point (4, 9). It fell on ground on x axis in 1 sec. Taking g = 10 m/s2 and all coordinate in metres. Find the X-coordinate where it fell. (A) (3, 0) (B) (4, 0) (C) (2, 0) (D) ( 2 , 0) 3. Three stones A, B, C are projected from surface of very long inclined plane with equal speeds and different angles of projection as shown in figure. The incline makes an angle with horizontal. If HA, HB and HC are maximum height attained by A, B and C respectively above inclined plane then : (Neglect air friction) (A) H + H = H (B) H2 H2 H2 A C B A C B (C) H + H = 2H (D) H2 H2 2H2 A C B A C B 4. A ball is thrown from bottom of an incline plane at an angle from the inclined surface up the plane. Another ball is thrown from a point on the inclined plane with same speed and at same angle from the inclined surface down the plane. If in the two cases, maximum height attained by the balls with respect to the inclined surface during projectile motion are h1 and h2 then : (A) h1 > h2 (B) h1 < h2 (C) h1 = h2 (D) All the three can be possible 5. A particle is projected from surface of the inclined plane with speed u and at an angle with the horizontal. After some time the particle collides elastically with the smooth fixed inclined plane for the first time and subsequently moves in vertical direction. Starting from projection, find the time taken by the particle to reach maximum height. (Neglect time of collision). 2u cos (A) g u (sin cos) (C) g 2u sin (B) g 2u (D) g 6. Two stones A and B are projected from an inclined plane such that A has range up the incline and B has range down the incline. For range of both stones on the incline to be equal in magnitude, pick up the correct condition. (Neglect air friction) (A) Component of initial velocity of both stones along the incline should be equal and also component of initial velocity of both stones perpendicular to the incline should be equal. (B) Horizontal component of initial velocity of both stones should be equal and also vertical component of initial velocity of both stones should be equal. (C) Component of initial velocity of both stones perpendicular to the incline should be equal and also horizontal component of initial velocity of bo

- 1. PART - I : OBJECTIVE QUESTIONS Single choice type 1. A bomber plane moving at a horizontal speed of 20 m/s releases a bomb at a height of 80 m above ground as shown. At the same instant a Hunter of negligible height starts running from a point below it, to catch the bomb with speed 10 m/s. After two seconds he realized that he cannot make it, he stops running and immediately holds his gun and fires in such direction so that just before bomb hits the ground, bullet will hit it. What should be the firing speed of bullet. (Take g = 10 m/s2 ) 80 m Ground 10 m/s 20 m/s (A) 10 m/s (B) 10 20 m/s (C) 10 10 m/s (D) None of these 2. A particle is projected from a point (0, 1) on Y-axis (assume + Y direction vertically upwards) aiming towards a point (4, 9). It fell on ground on x axis in 1 sec. Taking g = 10 m/s2 and all coordinate in metres. Find the X-coordinate where it fell. (A) (3, 0) (B) (4, 0) (C) (2, 0) (D) ( 5 2 , 0) 3. Three stones A, B, C are projected from surface of very long inclined plane with equal speeds and different angles of projection as shown in figure. The incline makes an angle with horizontal. If HA, HB and HC are maximum height attained by A, B and C respectively above inclined plane then : (Neglect air friction) A B C (A) HA + HC = HB (B) 2 B 2 C 2 A H H H (C) HA + HC = 2HB (D) 2 B 2 C 2 A H 2 H H 4. A ball is thrown from bottom of an incline plane at an angle from the inclined surface up the plane. Another ball is thrown from a point on the inclined plane with same speed and at same angle from the inclined surface down the plane. If in the two cases, maximum height attained by the balls with respect to the inclined surface during projectile motion are h1 and h2 then : (A) h1 > h2 (B) h1 < h2 (C) h1 = h2 (D) All the three can be possible 5. A particle is projected from surface of the inclined plane with speed u and at an angle with the horizontal. After some time the particle collides elastically with the smooth fixed inclined plane for the first time and subsequently moves in vertical direction. Starting from projection, find the time taken by the particle to reach maximum height. (Neglect time of collision). (A) g cos u 2 (B) g sin u 2 (C) g ) cos (sin u (D) g u 2
- 2. 6. Two stones A and B are projected from an inclined plane such that A has range up the incline and B has range down the incline. For range of both stones on the incline to be equal in magnitude, pick up the correct condition. (Neglect air friction) A B (A) Component of initial velocity of both stones along the incline should be equal and also component of initial velocity of both stones perpendicular to the incline should be equal. (B) Horizontal component of initial velocity of both stones should be equal and also vertical component of initial velocity of both stones should be equal. (C) Component of initial velocity of both stones perpendicular to the incline should be equal and also horizontal component of initial velocity of both stones should be equal in magnitude. (D) None of these. More than one choice type 7. A particle is projected from a point on the ground with an initial velocity of u = 50 m/s at an angle of 53° with the horizontal (tan 53° = 4/3, g = 10 m/s2 = acceleration due to gravity). (A) The velocity of the particle will make angle 45° with the horizontal after time 1 s. (B) The velocity of the particle will make angle 45° with the horizontal after time 7 s. (C) The average velocity between the point of projection and the highest point on its path is horizontal. (D) The average velocity between two points on same height will be horizontal. 8. Two stones are projected from level ground. Trajectories of two stones are shown in figure. Both stones have same maximum heights above level ground as shown. Let T1 and T2 be their time of flights and u1 and u2 be their speeds of projection respectively (neglect air resistance). Then y x 1 2 (A) T2 > T1 (B) T1 = T2 (C) u1 > u2 (D) u1 < u2 9. At the same instant, two boys throw balls A and B from the window with speeds 0 and k0 respectively, where k is constant. They collide in air at time t. Which of the following options is/are correct. (A) k = 1 2 cos cos (B) k = 1 2 sin sin (C) t = ) sin v sin kv ( h 2 0 1 0 (D) t = ) cos v cos kv ( h 2 0 1 0
- 3. PART - II : SUBJECTIVE QUESTIONS 1. Two ships A and B are stationary, facing away from each other. Ship A has a cannon at its back which fires shell's with a speed of 10 m/s. Initially they are at a distance 5 3 m apart. Find the maximum and minimum angle with which the shells should be projected from ship A to hit ship B. The ships are of equal length = 10 2 5 m. 2. A projectile aimed at a mark which is in the horizontal plane through the point of projection falls a cm short of it when the elevation is and goes b cm too far when the elevation is . Show that if the velocity of projection is same in all the case, the proper elevation is b a 2 sin a 2 sin b sin 2 1 1 3. A particle is thrown over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. If and be the base angles and the angle of projection prove that tan = tan + tan . 4. Some students are playing cricket on the roof of a building of height 20 m. While playing, ball falls on the ground. A person on the ground returns their ball with the minimum possible speed at angle 45° with the horizontal. Find out the speed of projection. 5. A shell bursts on contact with the ground and pieces from it fly in all directions with all velocities upto 80 feet per second. Show that a man 100 feet away is in danger for 2 5 seconds. [Use g = 32 ft/s2 ]. 6. A stone is thrown in such a manner that it would just hit a bird at the top of a tree and afterwards reach a maximum height double that of the tree. If at the moment of throwing the stone the bird flies away horizontally with constant velocity and the stone hits the bird after some time. Calculate the ratio of horizontal velocity of stone to that of the bird. 7. A body is thrown from the surface of the Earth at an angle to the horizontal with the initial velocity v0 . v0 << ve ve , (escape velocity of earth). Assuming the air drag to be negligible, find : (a) the time of motion ; (b) the maximum height of ascent and the horizontal range ; at what value of the angle they will be equal to each other ; (c) the equation of trajectory y (x), where y and x are displacements of the body along the vertical and the horizontal respectively ; 8. A cannon fires successively two shells with velocity v0 = 250 m/s; the first at the angle 1 = 53° and the second at the angle 2 = 37° to the horizontal, in the same vertical plane, neglecting the air drag, find the time interval between firings leading to the collision of the shells. (g = 10 m/s2 ). 9. A stone is projected horizontally from a point P, so that it hits the inclined plane perpendicularly. The inclination of the plane with the horizontal is and the point P is at a height h above the foot of the incline, as shown in the figure. Determine the velocity of projection. 10. Two parallel straight lines are inclined to the horizontal at an angle . A particle is projected from a point mid way between them so as to graze one of the lines and strikes the other at right angles. Show that if is the angle between the direction of projection and either of lines, then tan = 1 – 2 cot 11. The benches of a gallery in a cricket stadium are 1 m high and 1 m wide. A batsman strikes the ball at a level 1 m about the ground and hits a ball. The ball starts at 35 m/s at an angle of 53º with the horizontal. The benches are perpendicular to the plane of motion and the first bench is 110 m from the batsman. On which bench will the ball hit. 12. A ship is approaching a cliff of height 105 m above sea level. A gun fitted on the ship can fire shots with a speed of 110 ms1 . Find the maximum distance from the foot of the cliff from where the gun can hit an object on the top of the cliff. [ g = 10 m/s2 ]
- 4. PART-I 1. (C) 2. (C) 3. (A) 4. (C) 5. (C) 6. (C) 7. (A), (B), (D) 8. (B), (D) 9. (A), (C) PART-II 1. 30º & 60º 2. = b a 2 sin a 2 sin b sin 2 1 1 3. tan = tan + tan . 4. umin = 2 20 m/s 5. 2 5 sec. 6. 1 2 : 2 7. (a) = 2 (v0 / g) sin, (b) h = (v0 2 / 2g)sin2 , = (v0 2 / g)sin2 , = 76º ; (c) y= xtan – (g / 2v0 2 cos2 )x2 8. 10 s 9. v0 = 2 2gh 2 cot 10. tan = 1 – 2 cot 11. 6th step 12. 1100 m