A trolley is moving horizontal `x - y` plane with a velocity of `36km//h` towards x-direction. When trolley is at `(100, 0, 0)` a bullet is fired with a muzzel velocity of `50sqrt(2)m//s` at angle of `45^(@)` with horizontal in a plane making `53^(@)` with x-axis as shown. After `5 sec` bullet splits into two equal part. One of the part strikes trolley `5 sec` after splitting. If the distance of other part from origin is `Mxx100sqrt(2)` at this instant then. `M` is : (Assume mass of bullet is very small in comparison to trolley).

Answer

8

Explanation

A trolley is ………….
Velocity of bullet with respect to ground
`= 40 hati + 40 hat j + 50 hatk`
Time of fight `= (2xx50)/(10) = 10 sec`
Range of centre of mass
`= (2xx40sqrt(2)xx50)/(10)=400sqrt(2)m`
coordinate centre of mass after `10 sec = (500, 400, 0)`
One of the particle will fall on trolley
Position of trolley at the end of `10 sec`.
`= (200, 0, 0)`
Position of other partiolo = `(800, 800, 0)`
distance `= 800 sqrt(2)m implies M = 8`