To solve this problem, we can analyze the motion of each stone separately and then determine the height of the tower based on their respective equations of motion.
Let's consider the stone thrown from the tower first. We'll assume it follows a parabolic trajectory due to being thrown horizontally. The key information we have for this stone is that it falls to the ground in the same amount of time it takes for the vertically thrown stone to reach the ground.
For the stone thrown horizontally, its vertical motion can be described using the equation:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Now, let's focus on the vertically thrown stone. We know that it falls for 1.6 seconds, and its initial velocity is 32 m/s. The equation to calculate its vertical distance covered is:
h = v0 * t + (1/2) * g * t^2
where v0 is the initial velocity, g is the acceleration due to gravity, and t is the time.
Since both stones hit the ground simultaneously, we can set their respective equations for height equal to each other:
(1/2) * g * t^2 = v0 * (t - 1.6) + (1/2) * g * (t - 1.6)^2
Simplifying this equation will allow us to solve for t and find the time it takes for both stones to hit the ground simultaneously.
After solving for t, we can substitute the value back into either of the height equations to determine the height of the tower.
Please note that the units used in this calculation are in meters and seconds, assuming no air resistance or other factors affecting the motion of the stones.