Tarzan in trouble - Kinematics

[tandoorichicken]

Tarzan is in trouble once again and Jane and Cheetah have to decide whether to try to bail him out. Jane and Cheetah (70kg combined) are perched on a cliff 10m above Tarzan (70kg) and can swing down on a vine and grab him. To get to safety, they need to get to a perch 5m above Tarzan on the other side.

Determine the speed of Jane and Cheetah just before they would grab Tarzan. Assume no air drag or friction.

 

[HallsofIvy]

That should be fairly straight forward if you use "conservation of energy". Take Tarzan's position as 0 potential energy. Since they need to get to a position 5 m above Tarzan, where the potential energy of all 3 is 140g(5)= 700(9.81)= 6867 Joules, their total energy must be greater than 6867 Joules.
You know that the combined mass of Cheetah and Jane is 70 kg. so, taking V as their speed (in m/s) just before they "pickup" Tarzan, their kinetic energy is 35V² Joules. Since their potential energy is now 0, their total energy is 35V².

Solve 35V²= 6867.

 

[M98Ranger]

To determine the speed of Jane and Cheetah just before they grab Tarzan, we can use the equation for conservation of energy. Since there is no air drag or friction, all of the initial potential energy from being perched on the cliff will be converted into kinetic energy as they swing down on the vine.

The initial potential energy of Jane and Cheetah is given by mgh, where m is their combined mass of 70kg, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the cliff (10m).

PE = mgh
= (70kg)(9.8 m/s^2)(10m)
= 6860 Joules

This potential energy will be converted into kinetic energy, given by the equation KE = 1/2mv^2, where v is the velocity.

KE = 1/2mv^2
6860 = 1/2(70kg)v^2
v^2 = (2)(6860)/70
v = √196 m/s
v = 14 m/s

Therefore, the speed of Jane and Cheetah just before they grab Tarzan will be approximately 14 m/s. This is assuming they have a perfectly efficient swing and all of their potential energy is converted into kinetic energy. If there are any inefficiencies or losses, the actual speed may be slightly lower. But with this speed, they should be able to reach the perch 5m above Tarzan on the other side and save him from trouble.