Complete Question
The complete question is shown on the first uploaded image
Answer:
Part A
The velocity of Tarzan is [tex]v_T = 17.7 \ m/s[/tex]
Part B
The percentage loss of kinetic energy is %-loss [tex]= 61.4[/tex]%
Part C
The speed would be exactly the same
Explanation:
From the question we are told that
The mass of Tarzan is [tex]m = 85.5 \ kg[/tex]
The height of the cliff is [tex]h = 16.0 \ m[/tex]
From the law of conservation of energy
[tex]PE = KE[/tex]
Where PE is the potential energy of Tarzan at the top of the cliff which is mathematically represented as
[tex]PE = mgh[/tex]
KE is the kinetic energy of Tarzan as he swings toward jane and is mathematically represented as
[tex]KE = \frac{1}{2} mv^2_T[/tex]
So
[tex]mgh = \frac{1}{2}m v_T^2[/tex]
=> [tex]gh = \frac{1}{2} v_T^2[/tex]
Substituting values
[tex]9.8 * 16 = \frac{1}{2} v_T^2[/tex]
=> [tex]v_T = \sqrt{\frac{9.8 * 16}{0.5} }[/tex]
[tex]v_T = 17.7 \ m/s[/tex]
From the question we are told that the actual velocity of Tarzan is
[tex]v = 11 m/s[/tex]
The kinetic energy at the the velocity is mathematically represented as
[tex]KE_A = \frac{1}{2} m v^2[/tex]
Substituting values
[tex]KE_A = \frac{1}{2} (85) * 11^2[/tex]
[tex]KE_A = 5142.5 J[/tex]
The kinetic energy at [tex]v_T[/tex] is
[tex]KE = \frac{1}{2} * 85 * 17.7^2[/tex]
=> [tex]KE = 13314.83\ J[/tex]
Now the percentage loss of kinetic energy is mathematically evaluated as
%-loss [tex]= \frac{KE - KE_A}{KE} * 100[/tex]
substituting values
%-loss [tex]= \frac{13314.83 - 5142.5}{13314.83} * 100[/tex]
%-loss [tex]= 61.4[/tex]%
The mass of Tarzan does not affect the speed because looking at this equation
[tex]gh = \frac{1}{2} v_T^2[/tex]
We see that the velocity of Tarzan is not dependent on the mass of Tarzan
