A stone is dropped from the top of an overhead water tank and at the same time another stone is thrown vertically upwards from the ground level with a velocity of 20 ms^-1. If the stones met exactly 2 seconds after their release, determine the height of the overhead tank.

To solve this problem, we need to use the equations of motion.

1. Let's denote the height of the tank as h. The stone that is dropped from the top of the tank will fall under the acceleration due to gravity, which is approximately 9.8 m/s^2. The distance it falls in 2 seconds can be calculated using the equation of motion:

   h1 = 0.5 * g * t^2 h1 = 0.5 * 9.8 * (2)^2 h1 = 19.6 m

2. The stone that is thrown upwards from the ground level will first rise and then start falling back. The maximum height it reaches can be calculated using the equation:

   h2 = u * t - 0.5 * g * t^2 h2 = 20 * 2 - 0.5 * 9.8 * (2)^2 h2 = 40 - 19.6 h2 = 20.4 m

3. The total height of the tank is the sum of the distances each stone travelled before they met.

   h = h1 + h2 h = 19.6 m + 20.4 m h = 40 m

So, the height of the overhead tank is 40 meters.

To solve this problem, we need to use the equations of motion.

1. Let's consider the stone that is dropped from the top of the tank first. Since it is dropped, its initial velocity (u1) is 0. We know that the acceleration due to gravity (g) is 9.8 m/s^2. The time (t) it takes for the stones to meet is given as 2 seconds. We can use the equation of motion, s = ut + 0.5gt^2, to find the distance it falls. Substituting the known values, we get:

   s1 = u1t + 0.5gt^2 s1 = 02 + 0.59.82^2 s1 = 19.6 m

2. Now, let's consider the stone that is thrown upwards. Its initial velocity (u2) is given as 20 m/s. The acceleration due to gravity (g) is -9.8 m/s^2 (negative because it's acting against the motion of the stone). The time (t) it takes for the stones to meet is again 2 seconds. We can use the same equation of motion to find the distance it travels. Substituting the known values, we get:

   s2 = u2t + 0.5gt^2 s2 = 202 + 0.5*(-9.8)*2^2 s2 = 40 - 19.6 s2 = 20.4 m

3. The height of the tank is the sum of the distances travelled by both stones, so:

   h = s1 + s2 h = 19.6 m + 20.4 m h = 40 m

So, the height of the overhead tank is 40 meters.