Please help!!

We can determine the time it would take an object to fall (if there were no air resistance) by using the formula where d is the distance.t=1/4sq.root of d, d being the distance

1. We can determine the time it would take an object to fall (if there were no air resistance) by using the formula where d is the distance.

A. How long does it take a quarter dropped from a 35 foot roof to reach the ground?

B. If there are 5,280 feet in one mile, how long would it take an object to fall miles?


C. If it takes an object 5.9 seconds to fall d feet, how tall is the object?

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.

Sure! Let's break down each question step by step:

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 given formula t = 1/4 * sqrt(d). In this case, d is the distance, which is 35 feet. Let's substitute the value into the formula:

t = 1/4 * sqrt(35)

Now, we can calculate the time:

t ≈ 1/4 * 5.92

Simplifying further:

t ≈ 5.92/4

t ≈ 1.48 seconds

Therefore, it would take approximately 1.48 seconds for a quarter to reach the ground.

B. To determine how long it would take for an object to fall a certain number of miles, we need to know the value of "d" in the formula t = 1/4 * sqrt(d). In this case, the "d" is the distance, which is given in the question as "miles." However, the question does not specify the exact number of miles. Without this information, we cannot calculate the time.

C. In this question, the time taken by an object to fall "d" feet is given as 5.9 seconds. We need to find the height or distance "d" using the given formula t = 1/4 * sqrt(d). Rearranging the formula, we get:

d = (4*t)^2

Let's substitute the given time value into the formula:

d = (4*5.9)^2

Simplifying further:

d = 23.6^2

d ≈ 556.96 feet

Therefore, the object is approximately 556.96 feet tall.