Question

Supposed you were standing beneath a palm tree when a coconut began to fall. If the height of the coconut is 64 feet, how much time do you think you'd have to escape?

Answer 1

Answer:

t = 1.41 seconds

Step-by-step explanation:

We know the height at which the coconut is, which is 64 ft, now assuming that we are on the ground, we know that gravity is equal to 32.1742 ft / s².

Gravity is an acceleration, we have that the acceleration is equal to:

a = v / t

but the speed v = d / t, replacing we have:

a = (d / t) / t

That is to say

a = d / t²

Now, solved for you we have:

t = (d / a) ^ (1/2)

Replacing the values, we are left with:

t = (64 / 32.17) ^ (1/2)

t = 1.41 seconds

therefore, the person has 1.41 seconds to escape.

Answer 2

Answer:

The time, t, available to escape is 1.994 s ≈ 2 seconds.

Step-by-step explanation:

To solve the question, we note the given variables as follows

Height of tree = 64 feet = ‪19.5072‬ m

Also, the equation of motion of an object in free fall is given as

h = u·t + $\frac{1}{2}$·g·t²

Where:

t = Time for the object to fall through h

u = Initial velocity of the object  = 0 m/s

g = Acceleration due to gravity = 9.81 m/s²

h = Height from which the object is falling = 64 ft = ‪19.5072‬ m

Therefore

19.5072 m = 0 m/s × t + $\frac{1}{2}$×9.81 m/s²×t²

19.5072 m = 4.905 m/s²·t²

19.5072 m ÷  4.905 m/s² = t²

3.977 s² = t²

t = 1.994 s