Respuesta :
Given data
*The given mass of the ball is m = 5 kg
*The given height above the ground is h = 40 m
*The value of the acceleration due to the gravity is g = 9.8 m/s^2
*The given time is t = 1 minute = 60 s
(a)
The formula for the potential energy of the ball is given as
[tex]U_p=mgh[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} U_p=(5)(9.8)(40)_{} \\ =1960\text{ J} \end{gathered}[/tex]Hence, the potential energy of the ball is U_p = 1960 J
(b)
The formula for the power is given as
[tex]P=\frac{mgh}{t}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} P=\frac{5\times9.8\times40}{60} \\ =32.66\text{ W} \end{gathered}[/tex]Hence, the power is P = 32.66 W
(c)
When the ball is dropped from the height, the ball possess the kinetic energy. As the ball is moving or approaching with a speed towards the ground.
(d)
The formula for the speed of the ball hit the ground is given by the conservation of energy as
[tex]\begin{gathered} U_p=U_k \\ mgh=\frac{1}{2}mv^2 \\ v=\sqrt[]{2gh} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v=\sqrt[]{2\times9.8\times40} \\ =28\text{ m/s} \end{gathered}[/tex]Hence, the speed of the ball hit the ground is v = 28 m/s
