# Question #43d72

##### 2 Answers

62.8 meters

#### Explanation:

If

And at earth's surface this is a constant 9.81 meters per second per second. (rounding to 3 significant digits because that's what we did on our slide rules oh-so-many years ago.)

then

We're saying -9.81t because we're assigning negative values to the downward direction, positive values to the upward direction.

We can calculate the value of constant c because we know the value of v at time 0: 12m/s.

so we now know that

We know the ball will travel upwards while decelerating, eventually reaching velocity 0 at the apex of its travel. We can solve for the time when this occurs:

We know that at time t = 2 * 1.22, or 2.44 seconds, the ball is back to it's original height, and is travelling downwards at 12 m/s. (We're ignoring wind resistance).

Since we're told that the ball's total flight time is 5 seconds, we know that it has

**At this point, we can start a completely new derivation.** We have known initial conditions v(0) = -12 m/s, and total elapsed time will be 2.56 seconds.

So we have velocity

...and we can integrate to find x(t):

...and we know that at time t = 2.56 the ball's height will be zero.

With this, we can solve for constant c, which will be the tower's height (and the ball's height at time t = 0).

c = 62.8 meters. (rounded to 3 significant digits in all calculations)

...and you can see that we sidestepped the need to calculate the max height that the ball reached.

#### Explanation:

Setting the ball at the origin and using the convention "up is positive" we can use:

This becomes:

This means the height of the tower can be rounded to 63 m.