## Question

A gun is fired from a moving platform and the ranges of the shot are observed to be *R* and *S *when platform is moving forward or

backward respectively with velocity *V.* find the elevation of the gun is

### Solution

Let *u* and *v* be the horizontal and vertical component of velocity when the platform is at rest.

When the platform is moving forward, the resultant horizontal velocity is =*u* + *V* and vertical is *v*. The range *R* is given by

When the platform is moving backward with velocity *V*, the horizontal and vertical components of the velocity of the shot are *u* – *V* and *v*respectively.

The range is then

From Eqns. (1) and (2), *R * + *S* = 4*uv/g*

and *R – S =4Vv/g*

If α be the angle of projection, then

#### SIMILAR QUESTIONS

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be

The maximum height attained by a projectile is increased by 10% by changing the angle of projection, without changing the speed of projection. The percentage increase in the time of flight will be

The speed of projection of projectile is increased by 5%, without changing the angle of projection. The percentage increase in the range will be

A projectile has the same range *R* when the maximum height attained by it is either *h*_{1} or *h*_{2}. Then *R*, *h*_{1} and *h*_{2} will be related as

A relief aeroplane is flying at a constant height of 1960 *m* with speed 600*km/hr* above the ground towards a point directly over a person struggling in flood water (see fig.). At what angle if sight, should the pilot release a survival kit if it is to reach the person is water? (*g* = 9.8 m/s^{2})

At a harbour enemy ship is at a distance from the security cannon having a muzzle velocity of 60 m/s (a) To what angle must the cannon be elevated to hit the ship? (b) What is the time of flight? (c) How far should the ship be moved away from its initial position so that it becomes beyond the range of the cannon? (g = 10 m/s^{2})

During volcanic eruption chunks of solid rock are blasted out of the volcano. (a) At what initial speed would a volcanic object have to be ejected at 37° to the horizontal from the vent *A* in order to fall at *B* as shown in fig. (b) What is the time of flight? (g = 9.8 m/s^{2})

A gun, kept on a straight horizontal road, is used to hit a car travelling along the same road away from the gun with a uniform speed of 72 *km/hr*. The car is at a distance is 500 *m* from the gun, when the gun is fired at an angle of 45° with the horizontal. Find (a) the distance of the car from the gun when the shell hits it; (b) the speed of projection of the shell from the gun. (g = 9.8 m/s^{2})

Particles *P* and *Q* of mass 20 *g* and 40*g* respectively are simultaneously projected from points *A* and *B* on the ground. The initial velocities of *P*and *Q* make 45° and 135° angles respectively with the horizontal *AB* as shown in the figure. Each particle has an initial speed of 49 m/s. The separation *AB* is 245 m. Both particles travel in the same vertical and plane and undergo a collision. After collision *P* retraces its path. Determine the position of *Q* when it hits the ground. How much time after the collision does the particle *Q* take to reach the ground? (Take g = 9.8 m/s^{2})