Question

Particles P and Q of mass 20 g and 40g respectively are simultaneously projected from points A and B on the ground. The initial velocities of Pand 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/s2)

                                                      

Solution

Correct option is

 

As the horizontal speed of two particles towards each other is same  they will meet at the middle of AB, i.e., at distance (245/2) = 122.5 from A towards B.

 

So AB is the range and as the collision takes place at the middle of AB, so it is at the highest point of the trajectory.

Now applying conservation of linear momentum at the highest point along horizontal direction keeping in mind,

            

                  

This gives vQ = 0, i.e., after collision, the velocity of Q at highest point is zero. So Q will fall freely under gravity and will hit the ground in the middle of AB, i.e., 122.5 m from A towards B.

So time taken by Q to reach ground,

                  

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

A projectile has the same range R when the maximum height attained by it is either h1 or h2. Then Rh1 and h2 will be related as

Q4

A relief aeroplane is flying at a constant height of 1960 m with speed 600km/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/s2

                                               

Q5

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/s2)

Q6

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/s2)

                                                  

Q7

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/s2)

Q8

 

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

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