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?

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

Image from: Pixabay Under CC0 Public Domain License

Solution:

Show me the final answer↓

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

 

Final Answers:

Height of building = 44.1 m

Velocity of ball before impact = 29.4 m/s

 

This question can be found in Engineering Mechanics: Dynamics, 13th edition, chapter 12, question 12-9.

Leave a comment

Your email address will not be published.