Question

A particle (A) is dropped from a height and another particle (B) is projected in horizontal direction with speed of 5 m/s from the same height then correct statement is :

• A. Particle (A) will reach at ground first with respect to particle (B)
• B. Particle (B) will reach at ground first with respect to particle (A)
• C. Both particles will reach at ground simultaneously
• D. Both particles will reach at ground with same speed

Answer 1

The Correct Option is C

To determine which particle reaches the ground first, we need to analyze the motion of both particles in the vertical direction.

1. Vertical Motion Analysis:

   • Both particles A and B are released from the same height.
   • Particle A is dropped, meaning its initial vertical velocity, u_y = 0.
   • Particle B is projected horizontally, so its initial vertical velocity is also u_y = 0.
   • Under the influence of gravity alone, both particles will accelerate at the same rate, g = 9.81 \, \text{m/s}^2, in the vertical direction.

2. Time to Reach the Ground:

   • The time taken for an object to reach the ground when dropped or projected horizontally from a height h is given by the equation of motion:
   • h = \frac{1}{2} g t^2
   • Solving for time t gives:
   • t = \sqrt{\frac{2h}{g}}
   • Since both particles start at the same height and fall under the same gravitational acceleration, the time t is the same for both A and B.

3. Horizontal Motion of Particle B:

   • Particle B has an initial horizontal velocity of 5 m/s.
   • This horizontal motion does not affect the time taken to reach the ground since the vertical and horizontal motions are independent in projectile motion.

4. Conclusion:

   • Both particles A and B will reach the ground simultaneously.
   • The correct answer is: Both particles will reach at ground simultaneously.