A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450√3 meter from point P observes that angle of elevation of the balloon is 60°. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

Solution (By Examveda Team)

$$\eqalign{ & \tan {60^ \circ } = \frac{{AP}}{{PO}} \cr & \sqrt 3 = \frac{{AP}}{{450\sqrt 3 }} \cr & AP = 450\sqrt 3 \times \sqrt 3 \cr & AP = 1350{\text{ m}} \cr & {\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}} \cr & = \frac{{1350{\text{ m}}}}{{6 \times 60\sec }} \cr & = \frac{{15}}{4} \cr & = 3.75{\text{ m/s}} \cr} $$