A Rajput soldier sits on a horse next to a river. Across the river there is a hill and atop the hill is a fortress. He sees a Mughal. Sitting on the fortress's top wall. There is a full moon, so he angrily shoots an arrow at an angle `53^(@)` relative to the horizontal. The arrow hits Mughal after a 2 second flight. The horizontal distance from Rajput to Mughal is 30 meters. The arrow is 3 meters above the river when Rajput shoots it.

(a) What is the original velocity , `vec(V)`, of the arrow when Rajput shoots it ?
(b) What is Mughal elevation above the river ?
(c) What is the flight direction of the arrow the instant before it strikes Mughal, i.e., what is the angle, `theta`, between its direction and the horizontal when it skins into Mughal's tender flesh ?

Answer

(a) With `hat(i)` to right and `hat(j)` up `vec(V)=(15hat(i)+20hat(j)) m//s`; (b) 23 meters ; (c) It is horizontal `theta+theta`