A man of mass 70 kg is sitting in a motor car. The car is moving with an acceleration of 5 m`cdot s^(-2)`. What is the gravitational force on the man?
[ g = 9.8 m`cdot s^(-2)`]

Explanation

Let the horizontal acceleration of the car be `vec(a)`.
The apparent acceleration due to gravity with respect to the car.
`" " vec(g.) = vec(g)-vec(a) = [ vec(g) + (-vec(a)) ] `
which is the resultant of the vectors `vec(g) and -vec(a)`.
`g. = sqrt(g^(2) + a^(2)) = sqrt((9.8)^(2) + 5^(2))`
`" "11 " m"cdot s^(-2)`
Force of gravitation on the man
`70 xx 11 = 770` N .
which acts in the direction of g..
[ The apparent weight of the man is, `W. = (770)/(9.8) = 78.6` kg ]