Answer:
Potential Energy at the top = 3.528 J
Kinetic Energy when reaching the ground = 3.528 J
Speed when hitting the ground: 5.94 [tex]\frac{m}{s}[/tex]
Explanation:
a) recall the formula for the potential gravitational energy: m*g*h
(mass times the acceleration of gravity times the height at which the object is located relative to ground)
In this case the mass is 0.2 kg, the Height is 1.8 m and gravity is 9.8 m/s^2. All these in Si units, so their product will also give SI units: Joules.
[tex]Potential\,Energy= m*g*h\\Potential\,Energy=0.2*9.8*1.8 \,J\\Potential\,Energy=3.528\,J[/tex]
b) As the pear reaches the ground, its Potential Energy has been converted in Kinetic Energy, therefore the pear's Kinetic Energy at reaching the ground is also: 3.528 J
c) To find the pear's speed we use the Kinetic Energy formula:
[tex]KE=\frac{1}{2} m\,v^2[/tex]
where v represents the pear's speed. We replace the appropriate values for our case: KE = 3.528 J, mass = 0.2 kg, and solve for the speed:
[tex]KE=\frac{1}{2} m\,v^2\\3.528\,J=\frac{1}{2} \,0.2\,kg\,v^2\\3.528\,J=0.1\,kg\,v^2\\v^2=\frac{3.528\,J}{0.1\,kg} \\v^2=35.28\,\frac{J}{kg}\\v=\sqrt{35.28}\, \frac{m}{s} \\v=5.94\,\frac{m}{s}[/tex]
