Question

The vertical falling distance of a ball is directly proportional to the square of the time of falling. The ball falls 80 meters in 4 seconds.
(a) Find the vertical falling distance in 6 seconds.
(b) If the ball is dropped from a height of 245 meters,find the time it takes to hit the ground.​

Answer 1

Step-by-step explanation:

Let's first come up with some variables, and then perform an English-to-Math translation to derive an equation.

d = distance an object falls

t = the time it falls

Imagine the object in hand, and t is measured by a stopwatch. The stopwatch starts at the moment the object is released; at this moment, t = 0. d is also equal to 0 when t = 0, since at the precise moment it is released, it hasn't fallen yet.

Now that we have the situation and variables defined, we can begin the English-to-Math translation:

"The distance a free falling object falls" "is" "directly proportional to" "the square of the time it falls"

d = k t2

Removing all of the blank space, we have

d = kt2.

We are also given a distance (d = 44) for a given time (t = 5). We can solve for k by substituting these values into our equation:

44 = k (52). Since 52 = 25,

44 = 25k. Divide both sides by 25:

44/25 = k.

So, our equation is now complete:

d = (44/25) * t2.

"How far will it have fallen in 6 seconds" means, what is d if t = 6? This is equivalent to putting 6 in place of t:

d = (44/25) * 62, or

d = (44/25) * 36.

Do the calculation by hand or calculator, and you have your answer.

Answer 2

Step-by-step explanation:

Let's first come up with some variables, and then perform an English-to-Math translation to derive an equation.

d = distance an object falls

t = the time it falls

Imagine the object in hand, and t is measured by a stopwatch. The stopwatch starts at the moment the object is released; at this moment, t = 0. d is also equal to 0 when t = 0, since at the precise moment it is released, it hasn't fallen yet.

Now that we have the situation and variables defined, we can begin the English-to-Math translation:

"The distance a free falling object falls" "is" "directly proportional to" "the square of the time it falls"

d = k t2

Removing all of the blank space, we have

d = kt2.

We are also given a distance (d = 44) for a given time (t = 5). We can solve for k by substituting these values into our equation:

44 = k (52). Since 52 = 25,

44 = 25k. Divide both sides by 25:

44/25 = k.

So, our equation is now complete:

d = (44/25) * t2.

"How far will it have fallen in 6 seconds" means, what is d if t = 6? This is equivalent to putting 6 in place of t:

d = (44/25) * 62, or

d = (44/25) * 36.