Explanation:
Eg = mgh
a. Eg = (2.00 kg) (9.8 m/s²) (12.0 m)
Eg = 235 J
b. Eg = (2.00 kg) (9.8 m/s²) (3.00 m)
Eg = 58.8 J
c. Eg = (2.00 kg) (9.8 m/s²) (4.50 m)
Eg = 88.2 J
d. When the coconut hits the bystander:
Ek = 235 J − 58.8 J = 176 J
When the coconut hits the ground:
Ek = 88.2 J − 0 J = 88.2 J
Ek is the greatest when the coconut hits the bystander.
The energy of the coconut at various heights are required.
235.44 J
58.86 J
88.29 J
[tex]E_k[/tex] is maximum when it hits the bystander.
m = Mass of coconut = 2 kg
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
Distances from the ground
[tex]h_t[/tex] = On the tree = 12 m
[tex]h_h[/tex] = Head of person = 3 m
[tex]h_m[/tex] = Bounced maximum height = [tex]3+1.5=4.5\ \text{m}[/tex]
Potential energy in the tree
[tex]E_g=mgh_t\\ =2\times 9.81\times 12\\ =235.44\ \text{J}[/tex]
Bystander head
[tex]E_g=mgh_h\\ =2\times 9.81\times 3\\ =58.86\ \text{J}[/tex]
Bounced maximum height
[tex]E_g=mgh_m\\ =2\times 9.81\times 4.5\\ =88.29\ \text{J}[/tex]
Kinetic energy is given by
[tex]E_k=\dfrac{1}{2}mv^2[/tex]
The velocity (v) of the coconut will be maximum after it has traveled the most distance downward.
When the coconut hits the person the distance it traveled was [tex]12-3=9\ \text{m}[/tex].
After it bounces up and comes down the downward distance traveled is 4.5 m.
Hence, [tex]E_k[/tex] is maximum when it hits the bystander.
Learn more:
https://brainly.com/question/22100887
https://brainly.com/question/23150083
