A ball is thrown from a point with a speed V₀ at an angle of projection . . .

Question : A ball is thrown from a point with a speed V₀ at an angle of projection θ. From the same point and at the same instance a person starts running with a constant speed V₀/√2 to catch the ball? If yes, what should be the angle of projection?
(a) Yes, 60°
(b) Yes, 30°
(c) No
(d) Yes, 45°

Doubt by Shruti 

Solution : 

In this question, the person would be able to catch the ball if the horizontal velocity of the ball will become person's constant speed since both have to cover equal distance in equal time ofcourse. 

Horizontal velocity of the ball (ux)
= ucosθ
V₀cosθ

Constant Speed of person = 
V₀/√2

According to Question 

Horizontal velocity of the ball = Constant Speed of person
 V₀cosθ = V₀/√2
cosθ = 1/√2
cosθ = cos45°
θ=45°

Yes, the person would be able to catch the ball if the angle of projection is 45°. So the correct answer is (d) 45°

Similar Question : A ball is thrown from a point with a speed V₀ at an angle of projection θ. From the same point and at the same instance a person starts running with a constant speed V₀/2 to catch the ball? If yes, what should be the angle of projection?
(a) Yes, 60°
(b) Yes, 30°
(c) No
(d) Yes, 45°

Ans : (a) Yes, 60°