Respuesta :
We are given that a ball is dropped from a height of 35 meters in a free fall and we are asked to determine its final velocity. To do this we will use the following equation of motion:
[tex]v^2_f-v^2_0=2ah[/tex]Where:
[tex]\begin{gathered} v_f\text{ = final velocity} \\ v_0=\text{ initial velocity} \\ a=\text{ acceleration} \\ h=\text{ height} \end{gathered}[/tex]Since the ball is dropped this means that the initial velocity is zero. Also, since we have a free-fall motion the acceleration is the same as the acceleration of gravity. Replacing these values we get:
[tex]v^2_f=2gh[/tex]Now we solve for the velocity by taking the square root to both sides:
[tex]v_f=\sqrt[]{2gh}[/tex]Now we replace the values for the gravity and height:
[tex]v_f=\sqrt[]{2(9.8\frac{m}{s^2})(35m)}[/tex]Solving the operations:
[tex]v_f=26.19\frac{m}{s}[/tex]Therefore, the final velocity is 26.19 meters per second.
Now we will determine the time it takes the ball to reach the ground. To do that we will use the following equation of motion:
[tex]v_f=v_0+gt[/tex]Since the initial velocity is zero the equation simplifies to:
[tex]v_f=gt[/tex]Now we divide by the acceleration of gravity:
[tex]\frac{v_f}{g}=t[/tex]Now we replace the values:
[tex]\frac{26.19\frac{m}{s}}{9.8\frac{m}{s^2}}=t[/tex]Solving the operations we get:
[tex]2.67s=t[/tex]Therefore, it takes 2.67s for the ball to reach the ground in free-fall.
