Question

A ball is dropped from a height of $49m$ from ground. The wind is blowing horizontally. Due to wind a constant horizontal acceleration is applied on the ball. Choose the correct statement(s). [Take $g = 9.8m{s^{ - 2}}$].
(A) Path of ball is a straight line
(B) Path of the ball is curved
(C) The time taken by the ball to reach the ground is $3.16s$.
(D) Actual distance travelled by the ball is more than 49 m.

Answer 1

Hint There are two accelerations applied on the ball. One is acceleration due to gravity which is vertically downward and another due to the wind which is horizontal. Then it covers some vertical as well as some horizontal distance.

Complete step by step solution
There are two acceleration on the ball one is vertically downward and one is horizontal, then the path of the ball is never a straight line it will be curved. Hence option A is wrong and Option B is correct.
Time taken by the ball to reach the ground is the same if there is no wind. Time taken is given by
$s = u + at$, where $s$ is given as $49m$, $u$ is zero ( initially ball is at rest) and $a = g$.
$t = \dfrac{s}{g} = \dfrac{{49}}{{9.8}} = 5\sec $
$t \ne 3.16\sec $
Then option C is also incorrect.
We know that, vertical distance covered by the ball is $49m$ and the ball also covers some distance in a horizontal direction due to wind. Then the distance covered by the ball is more than $49m$ and option D is correct.

Hence correct options are B and D.

Note Actual path of the ball is parabolic path. Speed of the ball is increased due to both of the accelerations. If there is no wind then the path of the ball is a vertical straight line.