A cubical box dimension `L = 5//4` m starts moving with an acceleration `veca = 0.5 ms^(-2) hati` form the state of rest. At the same time, a stone is thrown form the origin with velocity `vecV = v_1hati + v_2hatj - v_3hatk` with respect to earth. Acceleration due to gravity `vecg = 10ms^(-2)(-hatj)`. The stone just touches the roof of box and finally falls at the diagonally opposite point. then:

Options

A. `v_1 = 3/2`
B. `v_2 = 5`
C. `v_3 = 5/4`
D. `v_3 = 5/2`

Answer

A, B, C

Explanation

a,b,c. `H = (u_(2)^(y))/(2g) rArr u_y = V_2 = 5ms^(-1)`
`T = (2usintheta)/g = (2u_y)/g = 1s`
`L = u_xt - 1/2 a_xt^2`
`5/4 = u_x xx 1 - 1/2 xx (0.5) xx (1)^2 rArr u_x = V_1 = 3//2 ms^(-1)`
Along `z` axis `5/4 = u_z xx 1` rArr `v_z = 5/4 ms^(-1)` .