Motion In A Straight Line

Observers in different inertial frames always measure different time intervals between a pair of events. According to time dilation

The scenario is depicted in the diagram below.

A is the starting position for both balls in this figure. B represents the highest point that the initial ball might reach, and C represents the point of impact.
Given in the problem,
Time till the 1st ball collides with the 2nd ball (t₁)=t sec
Time till the 2nd ball collides with the 1st ball (t₂)=(t₁−2) sec
Assume the two balls collide t seconds later, with the height of the point of collusion (point) from the ground equal to x.
We obtain by applying the second equation of motion to the first ball
⇒
⇒ (In this case, gravity is the only external force acting on the ball.)
⇒ …………. (Equation 1)
We obtain by applying the second equation of motion to the second ball

⇒
⇒ x =
⇒ ……….. (Equation 2)
We obtain by substituting the value of x from equation 1 into equation 2.

⇒
⇒
⇒
⇒
⇒
Now, for calculating the distance of the point of collision from the ground (x) , we simply use the equation of speed for the second ball, i.e.
Speed=
⇒
⇒
⇒ x=117.6m
Hence, option D is the correct option.

Step 1: Use the equation of motion for velocity
The equation for the velocity of an object falling freely from a height is given by: where:
- is the final velocity,
- is the initial velocity (which is 0 for free fall),
- is the acceleration due to gravity,
- is the height from which the object is dropped.
Step 2: Substitute the given values Given:
- Initial velocity ,
- ,
- Height .
Substitute these values into the equation: Answer: Therefore, the velocity of the ball just before hitting the ground is . So, the correct answer is option (2).

Step 1: Use the equation of motion for vertical displacement
The height reached by an object thrown vertically upwards can be calculated using the following equation of motion: where:
- is the final velocity (which is 0 at the highest point),
- is the initial velocity,
- is the acceleration due to gravity,
- is the maximum height.
Step 2: Substitute the given values
Given:
- Initial velocity ,
- Final velocity (since the object comes to rest at the highest point),
- .
Substitute these values into the equation: Answer: Therefore, the body will rise to a height of . So, the correct answer is option (1).