To find the velocity with which the second stone was thrown, we can use the concept of free fall and the equations of motion under gravity. Here are the steps to solve the problem:
1. Calculate the time taken for the first stone to fall to the ground from a height of 80 m. This can be done using the equation: \( h = \frac{1}{2} g t^2 \), where \( h = 80 \) m is the height, \( g = 9.8 \, m/s^2 \) is the acceleration due to gravity, and \( t \) is the time taken. Solving for \( t \), we get \( t = \sqrt{\frac{2h}{g}} \).
2. Since the second stone is thrown 2 seconds later, it will take \( t - 2 \) seconds to reach the ground.
3. Now, we need to find the initial velocity with which the second stone was thrown. We can use the equation of motion: \( v = u + at \), where \( v \) is the final velocity (0 m/s at the ground), \( u \) is the initial velocity (what we need to find), \( a = g = 9.8 \, m/s^2 \) is the acceleration due to gravity, and \( t = t - 2 \) is the time taken.
4. Substituting the values into the equation, we get \( 0 = u + 9.8(t - 2) \). Solving for \( u \), we find the velocity with which the second stone was thrown.
By following these steps and calculations, you should be able to determine the velocity with which the second stone was launched.
