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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Rest and Motion Kinematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rest and Motion Kinematics

A ball is projected from a point on the floor at a speed of 15 m/s...

A ball is projected from a point on the floor at a speed of 15 m/s15 \text{ m/s} and an angle of 60^{}^{{}^{\circ}} with the horizontal. Decide whether it will hit a vertical wall 5 m5 \text{ m} away from the point of projection and perpendicular to the plane of projection without hitting the floor. Also determine if the answer will differ if the wall is 22 m22 \text{ m} away.

Options

  1. ANo, it will not hit the 5 m5 \text{ m} wall; No, the answer does not differ for the 22 m22 \text{ m} wall.
  2. BNo, it will not hit the 5 m5 \text{ m} wall; Yes, the answer differs for the 22 m22 \text{ m} wall.
  3. CYes, it will hit the 5 m5 \text{ m} wall; Yes, the answer differs for the 22 m22 \text{ m} wall.
  4. DYes, it will hit the 5 m5 \text{ m} wall; No, the answer does not differ for the 22 m22 \text{ m} wall.

Correct answer

C. Yes, it will hit the 5 m5 \text{ m} wall; Yes, the answer differs for the 22 m22 \text{ m} wall.

Step-by-step solution

The horizontal range of the projectile is given by R=u2sin⁡2θgR = \dfrac{u^2 \sin 2\theta}{g}.

Substituting the given values u=15 m/su = 15 \text{ m/s}, \theta = 60^{}^{{}^{\circ}}, and g=9.8 m/s2g = 9.8 \text{ m/s}^2:

R = \dfrac{(15)^2 \sin(120^{}^{{}^{\circ}})}{9.8} = \dfrac{225 \times \sqrt{3}}{2 \times 9.8} \approx 19.88 \text{ m}

Since the distance to the first wall is 5 m5 \text{ m}, which is less than the range (5 m<19.88 m5 \text{ m} < 19.88 \text{ m}), the ball will hit the wall before hitting the floor. Thus, the answer for the 5 m5 \text{ m} wall is Yes.

For the second wall at 22 m22 \text{ m}, the distance is greater than the range (22 m>19.88 m22 \text{ m} > 19.88 \text{ m}). The ball will hit the floor before reaching this wall. Thus, it will not hit the 22 m22 \text{ m} wall without hitting the floor first.

Therefore, it will hit the 5 m5 \text{ m} wall, and the answer differs for the 22 m22 \text{ m} wall.
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