Question

Two objects on sliding down from rest on a smooth fixed slope, the other being thrown from the point Q start their motion at the same instant. Both get to the point P at the same time and at the same speed Find the initial angle of throw from horizontal. B) 330 C) 47° D) 640 A) 00

Answer 1

For object down R: Range & h: : height Therefore speed v = squareroot 2 g h (1) time taken t_1: calculated as below s = 1/2 g sin theta times t_1^2 (theta slope of incline) rightarrow h/sin theta = 1/2 g sin theta times t_1^2 rightarrow h = g/2 times h^2/(R^2 + h^2) times t_1^2 (2) From (1) & (2) 4 (R^2 + h^2) = v^2 times t_1^2 rightarrow 4 (R^2 + (v^2/2 g)^2) = v^2 times t_1^2 rightarrow 4 (R^2 + (v^2/2 g)^2) = v^2 times t_1^2 (3) For projectile Let alpha: angle of throw t_1 = t_1 = z v sin alpha/g (4) & R = (v cos alpha) times t_1 = g t_1^2/2 tan alpha (5) From (3), (4) & (5) 4 times [(g t_1^2/2 tan alpha)^2 + ((g t_2/2 sin alpha/2 g)^2)^2] = (g t_1/2 sin alpha)^2 t_1^2 rightarrow 1/tan^2 alpha + 1/16 sin^4 alpha = 1/4 sin^2 alpha