Question

If Galileo drops a cannon ball from the 60 meter high) Leaning Tower of Pisa, how fast will it be moving when it hits the ground?

Answer 1

Answer:

When the ball hits the ground, the velocity will be -34 m/s.

Explanation:

The height and velocity of the ball at any time can be calculated using the following equations:

y = y0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

y = height of the ball at time "t".

y0 = initial height.

v0 = initial velocity.

t = time.

g = acceleration due to gravity. (-9.8 m/s² considering the upward direction as positive).

v = velocity at time "t".

If we place the origin of the frame of reference on the ground, when the ball hits the ground its height will be 0. Then using the equation of height, we can calculate the time it takes the ball to reach the ground:

y = y0 + v0 · t + 1/2 · g · t²

0 = 60 m + 0 m/s · t - 1/2 · 9.8 m/s² · t²

0 = 60 m - 4.9 m/s² · t²

-60 m / -4.9 m/s² = t²

t = 3.5 s

Now, with this time, we can calculate the velocity of the ball when it reaches the ground:

v = v0 + g · t

v = 0 m/s - 9.8 m/s² · 3.5 s

v = -34 m/s

When the ball hits the ground, the velocity will be -34 m/s.