Juan was on vacation in Italy, and one of this adventures, he went up the Pisa tower. He wants to know the tower height using Physics, so he drops a small stone that he has in his pocket and takes the time it lasts to reach the ground. What is the Pisa tower height according to his time measurements? And how fast does the stone crash to the ground?
To determine the height of the Pisa tower using physics, Juan can make use of the kinematic equations of motion. By dropping a small stone and measuring the time it takes to reach the ground, he can then use the equations to calculate the tower's height and the speed at which the stone crashes. Here's how he can do it:
1. Measure the time: Juan should drop the stone from the top of the tower and measure the time it takes to reach the ground. He can use a stopwatch or any accurate timing device for this purpose.
2. Calculate the time of flight: The stone is dropped, so it falls from rest. The equation that relates the height (h), time (t), and acceleration due to gravity (g) is given by h = 0.5gt². Rearranging this equation, we get t = √(2h/g), where √ represents the square root. Juan can substitute the measured time into this equation to calculate the time of flight (t).
3. Calculate the height: Once Juan has obtained the time of flight (t), he can plug it into the equation h = 0.5gt² to calculate the height (h) of the Pisa tower. The acceleration due to gravity (g) is approximately 9.8 m/s² on the surface of the Earth.
4. Calculate the speed: The speed of the stone when it crashes to the ground can be calculated using the equation v = gt, where v represents the velocity or speed. Juan can substitute the time of flight (t) into this equation to calculate the speed at which the stone crashes to the ground.
By following these steps, Juan can calculate both the height of the Pisa tower and the speed at which the stone crashes to the ground using the principles of physics.