The acceleration due to gravity on planet X is
one fifth that on the surface of the earth.
If it takes 4.6 s for an object to fall a certain
distance from rest on earth, how long would
it take to fall the same distance on planet X?
Answer in units of s
screw you
why dont you figure it out? You'll never survive the hood life
To solve this problem, we can use the formula for free fall:
d = (1/2) * g * t²
Where:
d is the distance or height of the fall,
g is the acceleration due to gravity, and
t is the time taken to fall.
Let's calculate the time it would take to fall the same distance on planet X:
Given:
acceleration due to gravity on planet X = 1/5 * (acceleration due to gravity on Earth)
time taken to fall on Earth (t₁) = 4.6 s
Since the acceleration due to gravity on planet X is one-fifth that on Earth, the equation becomes:
d = (1/2) * (1/5 * g) * t₂²
We can then set up the following equation to find t₂:
(1/2) * (1/5 * g) * t₂² = (1/2) * g * t₁²
Notice that the factors of (1/2) and g cancel out on both sides of the equation.
Simplifying the equation further, we get:
(1/5 * g) * t₂² = g * t₁²
Now, let's solve for t₂:
(1/5 * g) * t₂² = g * t₁²
Dividing both sides of the equation by g gives:
(1/5) * t₂² = t₁²
Multiplying both sides by 5 gives:
t₂² = 5 * t₁²
Taking the square root of both sides gives:
t₂ = √(5 * t₁²)
Now, substitute the value of t₁ (4.6 seconds) and calculate t₂:
t₂ = √(5 * (4.6)²)
t₂ = √(5 * 21.16)
t₂ = √(105.8)
t₂ ≈ 10.285 s
Therefore, it would take approximately 10.285 seconds for the object to fall the same distance on planet X.