Motion in a Plane · Question 1

A particle is thrown with a speed v from a point O at an angle with the horizontal plane such that it passes through the point P at a height of 1 m and horizontal distance of 5 m from O, as shown in the figure. If acceleration due to gravity is g ms-2, then the correct statement(s) is/are: [figure]

1. If = 45 , then v = 5 g2 ms-1.
2. If = 45 , the particle reaches its maximum height before it reaches P.
3. If = 30 , the particle reaches its maximum height after reaching P.
4. If = -1 ( 15 ), then v = 125 g ms-1.

Answer

(1) If = 45 , then v = 5 g2 ms-1., (2) If = 45 , the particle reaches its maximum height before it reaches P.

Solution

Trajectory: y = x - gx22v2 2 with x = 5, y = 1.

(A) = 45 : 1 = 5 - 25gv2 v2 = 25g4, v = 5 g2 — correct.

(B) Top point at x = v2 2 2g = 258 = 3.125 m < 5 m — correct.

(C) = 30 : 1 = 5 3 - 50g3v2 v2 8.83g; top at x = v2 60 2g 3.8 m < 5 m, i.e. before P — incorrect.

(D) = 15: 1 = 1 - gx22v2 2 needs v ; no finite v — incorrect.

Answer: (A), (B)