# Free fall problems

These free fall problems will show you how to solve a variety of word
problems related to objects that are falling from a certain height.

**Problem #1**: A ball is thrown straight up in the air as shown in the figure above. If it takes the ball 2 seconds to reach its maximum height, what is the initial velocity?

**Solution**

When in the air, the ball is under the influence of gravity.

On the way up, the speed of the ball will decrease by 10 m / s each second until it reaches a speed of 0 ( maximum height)

The initial speed must have been 20 m / s.

You could also use the equation v = v

_{0} + g × t
and v

_{0} is the initial velocity.

0 = v

_{0} + 10 × 2

0 = v

_{0} + 20

Since 0 = -20 + 20, v

_{0} = -20

Why do we have a negative?

The equation v = v

_{0} + g × t is missing something important.

The value g = 10 m / s

^{2} is missing an important math concept.

There should be a negative next to g

v = v

_{0} + -g × t

0 = v

_{0} + -10 × 2

0 = v

_{0} + -20

Since 0 = 20 + -20, v

_{0} = 20

The value of g is just a measurement. In math anything upward the y-axis is positive. Since the acceleration is downward the y-axis, it should really be -g instead of just g.

Whenever you are solving free fall problems, keep the aforementioned in mind.

**Problem #2**: What is the instantaneous speed of a book dropped from the twenty-fifth floor after 2.5 second?

**Solution:** The formula that gets you the instantaneous speed is v = g × t.
Let us use g = 10 m / s

^{2}
t = 2.5 second

v = g × t = 10 m / s

^{2} × 2.5 s

v = 25 m /s

## Interesting free fall problems

Problem #3 :

How high is a building if it takes 5 seconds for a ball to hit the floor ?

Pretend the object was dropped from the rooftop and a man was holding the ball at a height of 1 meter before letting it go.

Use g = 10 m / s

^{2}
The formula to use is d =

g × t^{2}
/
2

Notice that when g = 10 m /s

^{2}, we can simplify the formula to 5 × t

^{2}
Since

10
/
2

= 5, we get d = 5 × t

^{2}
So, we can just use the formula above to simplify the problem.

d = 5 × 5

^{2}
d = 5 × 25

d = 125 meters.

However, the object was dropped from a height of 1 meter.

This is the height the man was holding the ball.

Therefore, subtract 1 from 125 to get the height of the building

h = 125 - 1 = 124.

The building is 124 meters.

This
is a very interesting free fall problem because it give us another very
efficient way to measure the height of a building.

**Problem #4: **Your turn to solve a free fall problem!

The world's tallest building is __Burj Dubai__**.** Rounded to the neatest 10, the building is 830 meters high. How long will it take an object to hit the floor?

Solve
this free fall problem yourself. I will not
solve it for you!