Freshly picked cucumbers are dropped into a bin from a height of 1.25 m above the bottom of the bin. Assuming that the bin is empty, how fast is a cucumber going when it hits the bottom of the bin? How much time does it take the cucumber to fall to the bottom of the bin?
Thanks!
To determine the speed at which the cucumber hits the bottom of the bin, we can use the equation for free fall:
v = √(2gh)
where:
v = velocity
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height
In this case, the height (h) is 1.25 m. Plugging in these values, we can calculate the speed:
v = √(2 * 9.8 * 1.25) ≈ 6.28 m/s
So, the cucumber is going approximately 6.28 m/s when it hits the bottom of the bin.
To find the time it takes for the cucumber to fall to the bottom of the bin, we can use another equation:
t = √(2h / g)
Using the same height (h) and acceleration due to gravity (g) values, we can calculate the time:
t = √(2 * 1.25 / 9.8) ≈ 0.51 seconds
So, it takes approximately 0.51 seconds for the cucumber to reach the bottom of the bin.
To find the speed at which the cucumber hits the bottom of the bin, we can use the principles of free-fall motion. We'll assume that the only force acting on the cucumber is gravity, neglecting any air resistance.
1. Find the time it takes for the cucumber to fall:
We can use the equation for the time of free-fall motion:
h = (1/2) * g * t^2 [Equation 1]
where h is the height, g is the acceleration due to gravity, and t is the time.
Since the height is given as 1.25 m, we have:
1.25 = (1/2) * 9.8 * t^2 [Substituting g = 9.8 m/s^2]
Solving for t, we find:
t^2 = (2 * 1.25) / 9.8
t^2 = 0.2541
t ≈ 0.504 s [Taking the square root since t > 0]
2. Calculate the speed at which the cucumber hits the bottom:
We can use the equation for the final velocity in free-fall motion:
v = g * t [Equation 2]
where v is the final velocity.
Substituting the value of t, we have:
v = 9.8 * 0.504
v ≈ 4.9392 m/s
Therefore, the cucumber will be going approximately 4.9392 m/s when it hits the bottom of the bin.
The time it takes for the cucumber to fall to the bottom is approximately 0.504 seconds.