In a football game, a player wants to throw a ball to his one of teammate, who is running on the field. Taken thrower position as origin and receiver initial position at `2hat(i) + 3hat(j)`, where `hat(i)` & `hat(j)` are in the plane of field. In subsequent run receiver displacement is `5hat(i)` then `8hat(j)`, then `–2hat(i) + 4hat(j)` then `–6hat(j)`. How far is receiver from thrower? (all displacements are in meter)

Options

A. `sqrt106`
B. `sqrt110`
C. `sqrt103`
D. `sqrt112`

Answer

A

Explanation

`bar r _(f) = vecr _(i) + Delta vec s _(1) + Delta vecs _(2) + ...`
`bar x _(f) = ( 2 hati + 3 hatj) + 5 hati + 8 hatj`
` + ( - 2 hati + 4 hatj ) + ( - 6 hatj )`
`barr _(f) = 5 hati + 9 hati `
` bar r _(f) = 5 hati + 9 hati `
Distance from thrower
`= sqrt ( 5 ^(2) + 9^(2)) = sqrt106`