If a person is thrown to a maximum height of 26.0 ft above
show calculations for
_______ s (time below 13.0 ft)
_______ s (time above 13.0 ft)
To calculate the time it takes for a person to be below 13.0 ft or above 13.0 ft, we need to consider the equation of motion for an object in free fall. The equation is given as:
h = vit + (1/2)gt^2
Where:
h - height of the object
vi - initial velocity of the object
g - acceleration due to gravity (typically taken as -32.2 ft/s^2)
t - time
Let's calculate the time below 13.0 ft:
First, we need to determine the initial velocity. Since the person is thrown upwards, the initial velocity will be positive. However, this information is not provided. Therefore, we will assume an initial velocity of 0 ft/s for simplicity.
Using this assumption, we rewrite the equation as:
13 = 0t + (1/2)(-32.2)t^2
Simplifying, we get:
16.1t^2 = 13
Dividing both sides by 16.1:
t^2 = 13 / 16.1
Taking the square root of both sides:
t ≈ √(13 / 16.1)
Using a calculator, we find:
t ≈ 0.89 seconds
Therefore, the time below 13.0 ft is approximately 0.89 seconds.
Now, let's calculate the time above 13.0 ft:
To find the time above 13.0 ft, we need to know the maximum height reached by the person. The maximum height is given as 26.0 ft.
Using this information, we rewrite the equation as:
26 = 0t + (1/2)(-32.2)t^2
Simplifying, we get:
16.1t^2 = 26
Dividing both sides by 16.1:
t^2 = 26 / 16.1
Taking the square root of both sides:
t ≈ √(26 / 16.1)
Using a calculator, we find:
t ≈ 1.22 seconds
Therefore, the time above 13.0 ft is approximately 1.22 seconds.