A stone is projected with an initial velocity v1 in a vertical plane at an angle ¥ to the horizontal and hits ground at A. another stone launched with initial veloc. v<sub>2</sub> at same angle but v<sub>2</sub> > v<sub>1</sub>. Let B(x2, y2) and C(x1,y1) be two points on the respective flight paths at the same time t. Show that gradient of segment BC is independant of time t. <B>Done</B>
When 2nd stone just clears a wall of hieght h, the first stone hits the ground at A. If the wall stands at point D on the level ground, prove that AD = hcot¥. <B>Done</B>
Further show that tan(-Ø) = tan¥ - [gt / (v2 cos¥)], where Ø is the angle made by the downward flight of the faster stone with the horizontal and T is the time of flights for the slower stone. Hence show v<sub>2</sub>(tan¥ + tanØ) = 2v<sub>1</sub>tan¥
EDIT: Ok i can show that tan(-Ø) = tan¥ - (gt/(V<sub>2</sub>cos¥)) which is kind of close, just 't' is not the time of flight of the slower stone, its just a time 't'. Hrmm