Two highways are perpendicular to each other imagine them to be along the x-axis and the y-axis, respectively. At the instant `t = 0`, a police car P is at a distance `d = 400 m` from the intersection and moving at speed of `8 km//h` towards it at a speed of `60 km//h` along they y-axis. The minimum distance between the cars is

Options

A. `300 m`
B. `240 m`
C. `180 m`
D. `120 m`

Answer

B

Explanation

If s be their separation at time t then,
`s^(2) = (0.4-80t)^(2) + (0.6-60t)^(2)`
where t is in hour, s in km. Minimise s using calculus.