two balls are dropped from different heights one ballis dropped 2sec after the other but they both strike the ground at same time 3sec after the first is dropped the difference of initial heights of the two balls will be

To solve this problem, we need to analyze the motion of both balls using the principles of physics, specifically the equations of motion under gravity. Let's break it down step by step.

Understanding the Scenario

We have two balls: Ball A and Ball B. Ball A is dropped first, and Ball B is dropped 2 seconds later. Both balls hit the ground at the same time, which is 3 seconds after Ball A is dropped. This means that Ball A is in free fall for 3 seconds, while Ball B is in free fall for only 1 second (since it is dropped 2 seconds later).

Calculating the Distance Fallen

We can use the formula for the distance fallen under gravity:

• d = 0.5 * g * t²

Here, d is the distance fallen, g is the acceleration due to gravity (approximately 9.81 m/s²), and t is the time in seconds.

Distance Fallen by Ball A

For Ball A, which falls for 3 seconds:

• d_A = 0.5 * g * (3)²
• d_A = 0.5 * 9.81 * 9
• d_A = 0.5 * 88.29
• d_A = 44.145 m

So, Ball A falls a distance of approximately 44.145 meters.

Distance Fallen by Ball B

For Ball B, which falls for only 1 second:

• d_B = 0.5 * g * (1)²
• d_B = 0.5 * 9.81 * 1
• d_B = 0.5 * 9.81
• d_B = 4.905 m

Thus, Ball B falls a distance of approximately 4.905 meters.

Finding the Difference in Initial Heights

Now, to find the difference in initial heights of the two balls, we simply subtract the distance fallen by Ball B from the distance fallen by Ball A:

• Difference in heights = d_A - d_B
• Difference in heights = 44.145 m - 4.905 m
• Difference in heights = 39.24 m

Therefore, the difference in the initial heights of the two balls is approximately 39.24 meters.

Summary

In summary, by applying the equations of motion, we determined that Ball A, dropped first, fell from a height of about 44.145 meters, while Ball B, dropped later, fell from a height of about 4.905 meters. The difference in their initial heights is approximately 39.24 meters. This illustrates how timing and height interact in free-fall scenarios under the influence of gravity.