# If it takes 3 s for a ball to strike the ground

If it takes 3 s for a ball to strike the ground when it is released from rest, determine the height in meters of the building from which it was released. Also, what is the velocity of the ball when it strikes the ground? Image from: Pixabay Under CC0 Public Domain License

#### Solution:

To figure out the height of the building, we will use the following kinematics equation:

$s_2=s_1+v_1t+\dfrac{1}{2}a_ct^2$

(Where $s_2$ is final displacement, $s_1$ is initial displacement, $v_1$ is initial velocity, $t$ is time, and $a_c$ is constant acceleration)

From the question, we know the following:

$s_1=0$ m

$v_1=0$ m/s

$a_c=9.81$ m/$s^2$

$t=3$ s

We will substitute these values into our equation.

$s_2=s_1+v_1t+\dfrac{1}{2}a_ct^2$

$s_2=0+0+\dfrac{1}{2}(9.81)(3^2)$

$s_2=44.1$ m

To figure out the velocity of the ball as it hits the ground, we will use the following equation:

$v_2=v_1+a_ct$

(Where $v_2$ is final velocity, $v_1$ is initial velocity, $a_c$ is constant acceleration and $t$ is time)

As before, we will substitute the values we know into the equation:

$v_2=v_1+a_ct$

$v_2=0+9.81(3)$

$v_2=29.4$ m/s