A staircase has five steps each 10 cm high and 10 cm wide. What is the minimum horizontal velocity to be given to the ball, so that it hits directly the lowest plane from the top of the staircase? ig = 10 ms-2)

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Q: 54 (NDA-II/2012)
A staircase has five steps each 10 cm high and 10 cm wide. What is the minimum horizontal velocity to be given to the ball, so that it hits directly the lowest plane from the top of the staircase? ig = 10 ms-2)

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,1,0,0,0,1,0

keywords: 

{'minimum horizontal velocity': [0, 0, 0, 1], 'lowest plane': [0, 0, 0, 1], 'staircase': [0, 0, 0, 1], 'steps': [0, 0, 0, 1], 'ball': [1, 3, 13, 12]}

To calculate the minimum horizontal velocity required for the ball to hit the lowest plane from the top of the staircase, we need to consider the motion of the ball in projectile motion. Since the ball experiences a constant acceleration due to gravity (g = 10 m/s^2), it will follow a parabolic path.

We can use the equation for the range of projectile motion to solve for the minimum horizontal velocity. The range of projectile motion is given by the equation R = (v^2*sin(2[REPLACEMENT]))/g, where v is the initial velocity of the projectile, [REPLACEMENT] is the angle of projection, and g is the acceleration due to gravity.

In this scenario, the angle of projection [REPLACEMENT] is 0 degrees (which corresponds to a horizontal projection) since the ball needs to hit the lowest plane directly. Therefore, sin(2[REPLACEMENT]) will be equal to sin(0) = 0.

Substituting sin(2[REPLACEMENT]) = 0 in the range equation gives us R = 0. This means that the horizontal distance covered by the ball will be zero.

Hence, the correct answer is option 3: 72 m/s.