Question

Solve the following problem.

A train is moving eastward at 10 m/sec. A waiter is walking eastward at 1.2m/sec; and a fly is charging toward the north across the waiter’s tray at 2 m/s. What is the velocity of the fly relative to Earth?

Answer 1

Given:
velocity of train w.r.t Earth, `vec"v"_"TE" = 10hat"i"`
velocity of waiter w.r.t train, `vec"v"_"WT" = 1.2hat"i"` 
velocity of fly w.r.t waiter, `vec"v"_"FW" = 2hat"j"`

∴ Velocity of fly with respect to Earth

`vec"v"_"FE" = vec"v"_"FT" - vec"v"_"ET"`

`= (vec"v"_"FW" - vec"v"_"TW") - vec"v"_"ET"`

`= 2hat"j" - (- 1.2 hat"i") - (- 10hat"i")`

`= 2hat"j" + 11.2hat"i"`   .....(considering north along +y axis)

Magnitude = `sqrt(11.2^2 + 2^2)`

= 11.38 m/s ≈ 11.4 m/s

Direction of velocity,

`theta = tan^-1 (2/11.2)~~ 10^circ` towards north of east.