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# Projectile Motion – Numerical Problems (Assignment for KV Pattom Class XI students)

The students are requested to start solving these numerical problems. More questions will be added till 8 pm on 13/09/2014. There will be more than 20 questions in all. All students are expected to solve at least 20 numericals among these. The deadline form submission is 15/09/2014.

1. A football player kick a ball at an angle of 37° to the horizontal with an initial speed of 15 m/s. Assuming that the ball travels in a vertical plane, calculate (i) the time at which the ball reaches the highest point. (ii) the maximum height reached by the ball (iii) the horizontal range of the projectile and (iv) the time for which the ball is in air.
2. A body is projected with a velocity of 20 m/s in a direction making an angle 60° with the horizontal. CCalculate (i) position after 0.5 seconds and  (ii) velocity after 0.5 seconds
3. The maximum vertical height of a projectile is 10 m. If the magnitude of the initial velocity is 28 m/s, what is the direction of the initial velocity? (g=9.8 m/s)
4. A bullet fired from a gun with a velocity of 140 m/s strikes the ground at the same level as the gun at a distance of 1 km. Find the angle of inclination with the horizontal at which the bullet is fired. (g=9.8 m/s)
5. A bullet is fired at an angle of 15° with the horizontal and hits the ground 6 km away. Is it possible to hit a target 10 km away by adjusting the angle of projection assuming the initial speed to be the same?
6. A cricketer can throw a ball to a maximum horizontal distance of 160 m. Calculate the maximum vertical height to which he can throw the ball. (g=10  m/s)
7. A football is kicked with 20 m/s at a projection angle of 45°. A receiver on the goal line 25 metres away in the direction of the kick runs the same instant to meet the ball. What must be his speed, if he is to catch the ball before it hits the ground?
8. A bullet fired at an angle of 60° with the vertical hits the ground at a distance of 2 km. Calculate the distance at which the bullet will hit the ground when fired at an angle of 45°, assuming the speed to be the same.
9. A person observes a bird on tree 39.6 m high and at a distance of 59.2m. With what velocity the person should shoot an arrow at an angle of 45° so that it may hit the bird?
10. A ball is thrown from the top of a tower with an initial velocity of 10 m/s at an angle of 30° with the horizontal. If it hits the ground at a distance of 17.3 m from the base of the tower, calculate the height of the tower. (Given g =10  m/s)
11. Prove that the time of flight T and the horizontal range R of a projectile are connected by the equation gT2 =2R tanθ, where θ is the angle of projection.
12. Show that the range of a projectile for two angles α and β is same if α+β=90°
13. A body is projected with velocity of 40 m/s. After 2 s it crosses a vertical pole of height 20.4 m. Calculate the angle of projection and horizontal range.
14. A plane is flying horizontally at a height of 1000 m with a velocity of 100 m/s when a bomb is released from it. Find (i) the time taken by it to reach the ground. (ii) the velocity with which the bomb hits the target and (iii) the distance of the target.
15. From the top of a building 19.6 m high a ball is projected horizontally. After how long does it strike the ground? If the line joining the point of projection to the point where it hits the ground makes an angle of 45° with the horizontal, what is the initial velocity of the ball.
16. A body is thrown horizontally from the top of a tower and strikes the ground after 2 seconds at an angle of 45° with the horizontal. Find the height of the tower and the speed with which the body was thrown. Take g =9.8 m/s)
17. A ball is projected horizontally from a tower with a velocity of 4 m/s. Find the velocity of the ball after 0.7 s. (Given g =10  m/s)
18. In between two hills of heights 100 m and 92 m respectively , there is a valley of breadth 16m. If a vehicle jumps from the first hill to the second, what must be the minimum horizontal velocity so that it may not fall into the valley? (Given g =10  m/s)
19. A mailbag is to be dropped into a post office from an aeroplane flying horizontally with a velocity of 270 km/h at a height of 176.4 m above the ground. How far must the aeroplane be from the post office at the time of dropping the bag so that the bag directly falls into the post office?
20. An aeroplane is flying in a horizontal direction with a velocity of 600 km/h and at a height of 1960 m. When it is above a point A on ground an object is dropped from it. The object strike the ground at the point B. Find the distance AB.
21. Two tall buildings are situated 200 m apart. With what speed must a ball be thrown horizontally from the window 540 m above the ground in one building so that it will enter a window 50 m above the ground in the other?

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