The time t (in seconds) that it takes for an object to fall a distance of s feet is given by the formula
t = radical symbol s /4
In some places, the Grand Canyon is one mile (5,280 feet) deep. How long would it take a stone dropped over the edge of the canyon to hit bottom?
would the answer be
18 seconds?
A falling object travels a distance given by the formula
d = 5t + 16t2,
where t is measured in seconds and d is measured in feet. How long will it take for the object to travel 21 ft?
To find the time it takes for the stone to hit the bottom of the Grand Canyon, we can substitute the given distance (s) into the formula:
t = sqrt(s/4)
For the Grand Canyon, the depth (s) is 5,280 feet or 1 mile. Substituting this value into the formula:
t = sqrt(5280/4)
t = sqrt(1320)
t ≈ 36.36 seconds
Therefore, it would take approximately 36.36 seconds for a stone dropped over the edge of the Grand Canyon to hit the bottom.
To find the time it takes for a stone to fall a distance of 5,280 feet (one mile) in the Grand Canyon, we can use the given formula:
t = sqrt(s) / 4
where t is the time in seconds and s is the distance in feet.
Plugging in the value of s = 5,280 feet into the equation we get:
t = sqrt(5,280) / 4
To simplify the equation, we need to find the square root of 5,280:
sqrt(5,280) ≈ 72.65
Now, we can substitute this value back into the equation:
t ≈ 72.65 / 4
Simplifying further, we get:
t ≈ 18.16
Therefore, it would take approximately 18.16 seconds for a stone to fall to the bottom of the Grand Canyon when dropped from the edge.