Question

Five balls A, B, C, D and E are projected with the same speed making angle
15°, 30°, 45°, 60° and 75° respectively with the horizontal. Which ball will strike
the ground at the farthest point?
(a) B (b) A
(c) E
(d) C
(e) D​

Answer 1

Answer:

a is the correct answer

Answer 2

Therefore the ball 'C' will strike the ground at the farthest point. (Option-d)

Given:

5 balls A, B, C, D, and E are projected with the same speed making an angle of 15°, 30°, 45°, 60°, and 75° respectively with the horizontal.

To Find:

The ball strikes the ground at the farthest point.

Solution:

The given question can be solved as shown below.

Given that,

5 balls A, B, C, D, and E are projected with the same speed making angles of 15°, 30°, 45°, 60°, and 75° respectively with the horizontal.

The horizontal range traveled by the ball is given by,

⇒ R = u² sin 2θ/g

Where u = initial velocity of the ball

g = Acceleration of the gravity

θ = Angle of the ball made with the horizontal.

In the question given, all the balls are projected with the same velocity.

So in the above equation, initial velocity and acceleration due to gravity are constants.

⇒ R ∝ sin 2θ

Hence the horizontal distance is maximum for the ball which has a sin 2θ maximum.

⇒ sin 2θ is maximum when θ = 45° then sin (2. 45°) = sin 90° = 1

So the ball 'C' which makes an angle of 45° will move to the farthest point.

Therefore the ball 'C' will strike the ground at the farthest point.

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