An aircraft moving horizontally at a speed of 80m/s and at a height of 500m releases a bomb to destroy a tank moving away from it. If the bomb is released when the tank is at a horizontal distance of 600m from the aircraft, find the speed of the tank.

To find the speed of the tank, we can use the concept of relative velocity. Relative velocity is the velocity of an object as observed from another moving object.

Let's break down the given information:
- The aircraft is moving horizontally at a speed of 80 m/s.
- The bomb is released at a height of 500 m.
- The tank is at a horizontal distance of 600 m from the aircraft when the bomb is released.

To solve this problem, we need to consider the horizontal motion of both the aircraft and the tank separately. Since the tank is moving away from the aircraft, its horizontal velocity will be subtracted from the horizontal velocity of the aircraft.

Here's how we can calculate the speed of the tank:

1. Find the time taken for the bomb to reach the tank.
- The bomb and the tank are in free fall, so they will both experience the same gravitational acceleration (9.8 m/s^2) vertically downwards.
- The height (h) at which the bomb is released is 500 m.
- The time taken (t) for the bomb to reach the ground can be found using the equation h = (1/2)gt^2.
- Plugging in the values: 500 = (1/2)(9.8)t^2.
- Solve for t: t^2 = (2 * 500) / 9.8, t^2 = 102.04, t ≈ 10.1 seconds.

2. Find the horizontal displacement of the tank during the time the bomb reaches the ground.
- The tank is 600 m away from the aircraft when the bomb is released.
- The aircraft and the tank are connected at that moment, so the horizontal displacement of the tank will be the horizontal velocity of the tank multiplied by the time taken for the bomb to reach the tank.
- The horizontal displacement (d) of the tank is equal to the speed of the tank (V) multiplied by the time (t).
- Plugging in the values: 600 = V * 10.1.
- Solve for V: V = 600 / 10.1 ≈ 59.4 m/s.

Therefore, the speed of the tank is approximately 59.4 m/s.