At `t = 1` sec., a particle is at `(1, 2, 0)`. It moves towards `(, -8, 10)` with a constant speed of `50 m//s`. The position of the particle is measured in metres and the times in sec. Assuming constant velocity, the position of the particle at `t = 4s` is :

Options

A. `51hat(i) - 98 hat(j) + 100 hat(k)`
B. `6 hat(i) - 8 hat(j) + 10 hat(k)`
C. `5hat(i) - 10 hat(j) + 10 hat(k)`
D. `50 hat(i) - 100 hat(j) + 100 hat(k)`

Answer

A

Explanation

`bar(S) = bar(V) xx t`
`bar(V) = |bar(V)| hat(V)`
`|bar(V)| = 50 m//s` and `hat(V) = (5 hat(i) - 10 hat(j) + 10 hat(k))/(15)`
`bar(S) = 50 ((5hat(i) - 10 hat(j) + 10 hat(k))/(15)) xx 3`
`= 50 hat(i) - 100 hat(j) 100 hat(k)`
`bar(S) = bar(r )_(f) - bar(r )_(1) = bar(r )_(f) - (hat(i) + 2 hat(j))`
`bar(r )_(f) = bar(S) + hat(i) + 2hat(j) = 51hat(i) - 98 hat(j) + 100 hat(k)`