A stone is dropped from the edge of a roof, and hits the ground with a velocity of -195 feet per second. How high is the roof? .
To determine the height of the roof, we can use the equations of motion for a freely falling object. The equation we need to use is:
v^2 = u^2 + 2aS
Where:
v = final velocity (in this case, -195 feet per second)
u = initial velocity (0 feet per second, since the stone is dropped)
a = acceleration due to gravity (-32.2 feet per second squared)
S = distance or height
Rearranging the equation to solve for S, we have:
S = (v^2 - u^2) / (2a)
Plugging in the given values, we get:
S = (-195^2 - 0) / (2 * -32.2)
Calculating this gives us:
S = (38025) / (-64.4)
Simplifying further:
S ā -590.37
Since the height cannot be negative, we take the absolute value, giving us the final answer:
The height of the roof is approximately 590.37 feet.
To determine the height of the roof, we can use the formula for the distance an object falls due to gravity:
š = (š£Ā² - š¢Ā²) / (2š)
Where:
š = distance
š£ = final velocity (in this case, -195 ft/s)
š¢ = initial velocity (0 ft/s, as the stone is dropped)
š = acceleration due to gravity (approximately -32.2 ft/sĀ²)
Plugging in the given values into the formula:
š = ((-195)Ā² - 0Ā²) / (2 * -32.2)
Simplifying the equation:
š = (38025) / (-64.4)
Finally, calculating the distance:
š ā 590.57 ft
Therefore, the height of the roof is approximately 590.57 feet.
v = at
that gets you t
d = 1/2 at^2
that gets you the height
or, d = v^2 / 2a
You have v=-195, a=-32