From the top of a tower of height 200 m, a ball A is projected up with 10 ms^1 and two seconds

step 1 Dear students, in the given problem, problem 48, the correct options are option A, B and D, opti

From the top of a tower of height 200 m, a ball A is...

From the top of a tower of height $200 \mathrm{~m}$, a ball $A$ is projected up with $10 \mathrm{~ms}^{1}$ and two seconds later another ball $B$ is projected vertically down with the same speed. Then, (a) both $A$ and $B$ will reach the ground simultaneously. (b) the ball $A$ will hit the ground 2 second later than $B$ hitting the ground. (c) both the balls will hit the ground with the same velocity. (d) both will rebound to the same height from the ground, if both have same coefficient of restitution.

From the top of a tower of height $200 \mathrm{~m}$, a ball $A$ is projected up with $10 \mathrm{~ms}^{1}$ and two seconds later another ball $B$ is projected vertically down with the same speed. Then,
(a) both $A$ and $B$ will reach the ground simultaneously.
(b) the ball $A$ will hit the ground 2 second later than $B$ hitting the ground.
(c) both the balls will hit the ground with the same velocity.
(d) both will rebound to the same height from the ground, if both have same coefficient of restitution.

Key Concepts

Projectile Motion

Projectile motion describes the motion of an object thrown into space under the influence of gravity, where its horizontal and vertical components of motion are analyzed separately. In vertical motion problems, such as moving upward or downward, the key equations of motion under uniform acceleration are used to determine position, velocity, and time to reach a certain point.

Time of Flight and Kinematics

Time of flight in vertical motion problems involves calculating how long an object takes to reach the ground or a certain height, taking into account its initial velocity, acceleration due to gravity, and initial position. The kinematic equations provide a framework to assess the effect of different initial conditions, including launch speed and delay in projection, on the duration of the flight.

Effect of Launch Conditions and Time Delays

In problems with varying launch conditions, such as different times of projection or different initial directions of motion, the analysis must consider how these factors alter the trajectory and impact time. Time delays between projections mean that objects might be influenced by gravity over different intervals, affecting when they reach a target, even if launched from the same height.

Final Velocity and Energy Considerations

Determining the final velocity with which an object impacts the ground involves understanding that gravitational acceleration acts uniformly regardless of the initial upward or downward motion. Due to energy conservation, objects starting from the same height under gravity (ignoring air resistance) may have identical impact speeds despite differing initial trajectories.

Coefficient of Restitution

The coefficient of restitution is a measure of how 'bouncy' a collision is, quantifying the ratio of speeds after and before an impact. It is crucial in determining the rebound height of an object after collision with a surface, as it directly relates to the energy retained or lost during the impact.

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