Question

Tarzan (mT=85.0 kg) is perched on a cliff 16.0 m above Jane. Jane is in the foreground is looking forwards. In the background, Tarzan has jumped off of a cliff and is swinging on a vine towards Jane. A red curved arrow points from Tarzan to Jane, showing the path he will swing on. Answer the three questions below, using three significant figures. Part A: What is the value of Tarzan's speed (vT) just as he gets down to Jane's level?

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

Part A

The velocity of Tarzan is   $v_T = 17.7 \ m/s$

Part B

The percentage loss of kinetic energy is  %-loss  $= 61.4$%

Part C

The speed would be exactly the same

Explanation:

From the question we are told that

       The mass of Tarzan is $m = 85.5 \ kg$

          The height of the cliff is $h = 16.0 \ m$

           

From the law of conservation of energy

             $PE = KE$

Where PE is the potential energy of Tarzan at the top of the cliff which is mathematically represented as

            $PE = mgh$

        KE is the kinetic energy of Tarzan as he swings toward jane and is mathematically represented as

           $KE = \frac{1}{2} mv^2_T$

  So

            $mgh = \frac{1}{2}m v_T^2$

=>        $gh = \frac{1}{2} v_T^2$

Substituting values

             $9.8 * 16 = \frac{1}{2} v_T^2$

=>           $v_T = \sqrt{\frac{9.8 * 16}{0.5} }$

             $v_T = 17.7 \ m/s$

From the question we are told that the actual velocity of Tarzan is

            $v = 11 m/s$

The kinetic energy at the the velocity is mathematically represented as

         $KE_A = \frac{1}{2} m v^2$

Substituting values

          $KE_A = \frac{1}{2} (85) * 11^2$

          $KE_A = 5142.5 J$          

The kinetic energy at $v_T$ is  

       $KE = \frac{1}{2} * 85 * 17.7^2$

=>     $KE = 13314.83\ J$

Now the percentage loss of kinetic energy is mathematically evaluated as

       %-loss  $= \frac{KE - KE_A}{KE} * 100$

substituting values

             %-loss  $= \frac{13314.83 - 5142.5}{13314.83} * 100$

                %-loss  $= 61.4$%

The mass of Tarzan does not affect the speed because looking at this equation

                $gh = \frac{1}{2} v_T^2$

We see that the velocity of Tarzan is not dependent on the mass of Tarzan