11. Determine the speed at impact in the following situations. Air resistance is
negligible.
(a) A seagull drops a shellfish onto a rocky shore from a height of 12.5 m to
crack the shell.
(b) A steel ball is dropped from the Leaning Tower of Pisa, landing 3.37 s later.
(a) To determine the speed at impact, we can use the equation for the final velocity in free fall:
vf = √(2gh)
Where vf is the final velocity, g is the acceleration due to gravity (approximated as 9.8 m/s²), and h is the height from which the object is dropped.
In this case, the height from which the seagull drops the shellfish is 12.5 m. Plugging this value into the equation, we have:
vf = √(2 * 9.8 * 12.5)
vf = √(245)
vf ≈ 15.65 m/s
So, the speed at impact when the seagull drops the shellfish is approximately 15.65 m/s.
(b) To determine the speed at impact, we can use the equation for displacement in free fall:
d = (1/2)gt²
Where d is the displacement, g is the acceleration due to gravity, and t is the time of free fall.
In this case, the time of free fall is given as 3.37 s. Plugging this value into the equation, we have:
d = (1/2) * 9.8 * (3.37)²
d = 52.08 m
Since the displacement is equal to the height from which the ball is dropped, the height from the Leaning Tower of Pisa is 52.08 m.
Now, we can use the equation for final velocity discussed in part (a):
vf = √(2gh)
Plugging in the values, we have:
vf = √(2 * 9.8 * 52.08)
vf = √(1020.288)
vf ≈ 31.98 m/s
So, the speed at impact when the steel ball is dropped from the Leaning Tower of Pisa and lands 3.37 s later is approximately 31.98 m/s.