A. To find the time it would take for a quarter dropped from a 35-foot roof to reach the ground, we can use the formula t = 1/4 * √d, where d is the distance.
Substituting the given value of d = 35, we get:
t = 1/4 * √35
Now, calculating the square root of 35, we get:
t ≈ 1/4 * 5.92
t ≈ 1.48 (rounded to two decimal places)
Therefore, it would take approximately 1.48 seconds for the quarter to reach the ground.
B. To find the time it would take an object to fall miles, we need to convert miles to feet. Since there are 5,280 feet in one mile, the distance (d) would be equal to miles multiplied by 5,280.
Let's assume the miles are denoted by the variable m, then:
d = m * 5,280
Now, we can use the formula t = 1/4 * √d to calculate the time.
Substituting the value of d as m * 5,280, we get:
t = 1/4 * √(m * 5,280)
t = √(m * 1,320)
Therefore, the expression for the time it would take an object to fall m miles is t = √(m * 1,320).
C. The given information states that it takes an object 5.9 seconds to fall d feet. To find the height (d) of the object, we can rearrange the formula as follows: d = (t/0.25)².
Substituting the given value of t = 5.9 seconds, we have:
d = (5.9/0.25)²
Now, performing the calculations inside the brackets first, we get:
d = (23.6)²
d = 556.96
Therefore, the object's height is approximately 556.96 feet.