The observation deck of tall skyscraper is 370. m above the time required for a penny to free fall from the deck to the street below and its velocity when it reaches the ground . Plzz help I know the t= .869 and the v= 85.2 and thank u :) have a good day plz answer this is a graded hw 😩
4.9t^2 = 370
v = 9.8t
To calculate the time required for a penny to free fall from the observation deck of a tall skyscraper to the street below, we can use the kinematic equation for free fall:
h = (1/2) * g * t^2
where:
h is the height (370 m),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
and t is the time.
To find the time (t), we need to rearrange the equation and solve for t. Let's substitute the given values:
370 m = (1/2) * 9.8 m/s^2 * t^2
Simplifying the equation:
370 = 4.9t^2
Now, divide both sides by 4.9:
370 / 4.9 = t^2
Using a calculator:
t^2 ≈ 75.51
To find t, we need to take the square root of both sides:
t ≈ √75.51
Using a calculator:
t ≈ 8.68 seconds (rounded to two decimal places)
Therefore, the time required for the penny to free fall from the observation deck to the street below is approximately 8.68 seconds (t ≈ 8.68 s).
Now, let's calculate the velocity (v) of the penny when it reaches the ground. We can use another kinematic equation:
v = g * t
where:
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time (8.68 s)
Substituting the values:
v = 9.8 m/s^2 * 8.68 s
Using a calculator:
v ≈ 85.2 m/s (rounded to one decimal place)
Therefore, the velocity of the penny when it reaches the ground is approximately 85.2 m/s (v ≈ 85.2 m/s).