Standing at a distance of 7 m from an 11.8 m high building, a healthy young man sees a kid slipping from the top floor. Determine the speed (assumed uniform) with which he should run to catch the kid at arms height ( 1.8 m ) in m/s.

Step-by-step solution

The distance fallen by the kid before being caught is: h = 11.8 - 1.8 = 10 m Using the second equation of motion for the freely falling kid ( u = 0 ): h = ut + 1 2 gt^2 10 = 0 + 1 2 9.8 t^2 10 = 4.9 t^2 t^2 = 10 4.9 = 100 49 t = 10 7 s The man must cover a horizontal distance of 7 m in this time t to catch the kid. Since his speed is uniform, the required speed v is: v = Distance Time = 7 10 7 v = 49 10 = 4.9 m/s