Problems on projectiles

1. The horizontal component of the velocity of a projectile is twice its initial vertical component. Find the range on the horizontal plane, if the projectile passes thought a point 18m horizontally and 3m vertically above the point of projection.(ans:- 27m)

2. A stone is projected upwards from the ground with velocity of 16m/s at an angle of 60o to the horizontal. With what velocity must another stone be projected at an angle of 45o to the horizontal from the same point in order : i. To have the same horizontal range?ii. To attain the same maximum height? (Ans:-14.89m/s,19.6m/s)

3. Maximum range of field gun is 2000m. If a target at a distance of 1200m is to be hit, what should be

the angle of projection?(Ans:- o or 71.565o)

4. A projectile is fired with a velocity of 300m/s at an upward angle of 60o to horizontal. Neglect air resistance determine:- 1) time of flight 2) range 3) its position after 35sec 4) its velocity after 35sec?

(Ans:- 1) t=52.97sec 2)R=7945.19m 3)x=5250m,y=3084.64m 4)171.69m/s at =29.116o to horizontal)

5. If a rifled gun fires a bullet with muzzle velocity of 237m/s. to strike the enemy at a horizontal distance of 5km and at a height of approximately 350m, what will be the angle of projection? (Ans: -

0 or 37.11o)

6. The maximum horizontal range of a gun is Rm. compute the firing angle to hit the enemy located at

half distance of maximum horizontal range.(Ans:- =15o)

7. Two bullets are fired from a defective rifled-gun. First one undershoots the target by 10m while it was projected at 170. Second bullet projected at 440 overshoots the target by 25m.Determine the correct angle of projection for killing the enemy.(Ans:-21.620)

8. A ball is thrown at a velocity v to clear two towers as shown in fig determine angle of projection and

the horizontal range in terms of the co-ordinates a and b?(ans:- tan and R=

)

9. An object of mass 6kgs is projected with a velocity of 25m/s at angle of 60o to the horizontal. At the highest point of its path, the projectile explodes and breaks up into two fragments of masses 2kg and 4kg and these fragments separate horizontally. The explosion releases internal energy such that the kinetic energy of the system at the highest point gets doubled. Calculate the distance of separation between the two fragments when they reach the ground?

10. A fire brigade man wants to extinguish a fire at a height of 6m above the nozzle standing at a distance of 5m away from the fire. Find 1) the minimum velocity of nozzle discharge required 2) velocity of discharge if the fire man could extinguish with angle of projection of 600?

11. A bullet is fired at an angle of 45o with the horizontal with a velocity of 275m/s how high the bullet will rise and what will be its horizontal range?