one body is dropped , while a second body is thrown downward with a initial velocity of 1m/s simultaneously. the separation between these is 18m after a time (a) 18s (b) 9 s (c) 4.5s (d) 36s

To tackle this problem, we need to analyze the motion of both bodies using the principles of kinematics. The first body is simply dropped from rest, while the second body is thrown downward with an initial velocity. We can use the equations of motion to determine the separation between the two bodies after a certain time.

Understanding the Problem

We have two bodies:

• Body A: dropped from rest (initial velocity = 0 m/s)
• Body B: thrown downward with an initial velocity of 1 m/s

Both bodies are subjected to the same gravitational acceleration, which is approximately 9.81 m/s². The separation after a certain time is given as 18 meters.

Equations of Motion

The equations of motion that we will use are:

• For Body A (dropped): s_A = ut + (1/2)gt²
• For Body B (thrown): s_B = ut + (1/2)gt²

Where:

• s is the distance traveled
• u is the initial velocity
• g is the acceleration due to gravity (9.81 m/s²)
• t is the time in seconds
• t will be the same for both bodies since they start simultaneously.

Calculating Distances

Let's calculate the distance traveled by each body after a time t.

Distance for Body A:

Since it is dropped from rest, its initial velocity u_A = 0

s_A = 0 + (1/2)(9.81)t² = 4.905t²

Distance for Body B:

For Body B, the initial velocity u_B = 1 m/s:

s_B = (1)t + (1/2)(9.81)t² = t + 4.905t²

Finding the Separation

The separation between the two bodies is defined as:

Separation = s_B - s_A

Substituting the expressions we derived:

Separation = (t + 4.905t²) - (4.905t²) = t

Thus, the separation between the two bodies is equal to the time t in seconds.

Setting Up the Equation

We know from the problem statement that this separation equals 18 m:

t = 18 m

This implies that t = 18 seconds.

Choosing the Correct Option

Now, let's look at the options provided:

• (a) 18s
• (b) 9s
• (c) 4.5s
• (d) 36s

The correct answer is (a) 18s, since that is the time at which the separation between the two bodies becomes 18 meters.

Summary

By applying the equations of motion for both bodies and calculating their respective distances, we deduced that the separation after 18 seconds is indeed 18 meters, confirming the correctness of our approach.