The component of vector `vecA = a_x hati +a_y hatj + a_z hatk` along the direction of 'hati - hatj'

Options

A. `a_x - a_y + a_z`
B. `a_x-a_y`
C. `(a_x-a_y) sqrt2`
D. `(a_x+a_y+a_z)`

Explanation

The maximum height "h" reached by a ball thrown vertically upwards can be obtained from equation of motion as follow,
`v=u-g t`
`implies u-"gt" ( :.v=0) ........(1)`
`v^2-u^2=-2gh^'`
`implies u^2=2gh`
`(g t)^2=2gh ......("from" "equation"(1)) ...(2)`
`h=(""g t""^2)/2` Similarly when a ball is falling downwards from the maximum height
`"S"=ut_1 + 1/2 "gt"_1^2`
`impliesh/2=(0)t_1+1/2 ""gt""_1^2`
`t_1=sqrt(h/g)=t/sqrt2`
`:.,"total time "=t+t_1=t+t/sqrt2=(1+1/sqrt2)t`