Question

Tarzan and jane, wholse toatl mass is 130 kg starts their swing on a 5m long vine is at an angle of 30 degree with the horizontal. At the bottom of the arc, Jan, whose mass is 50kg releases the vine. What is the maximum height at which Tarzan can land on a branch after his swing continues? (Hint: Treat Tarzan's and jane's energyies as separate quantities)

Answer 1

h' = 2.5 m

Step-by-step explanation:

combine mass of Tarzan and Jane, M= 130 Kg

height of vine = 5 m

angle made with horizontal = 30°

mass of Jane , m= 50 Kg

angle made with vertical = 60°

cos 60° = x/5

x = 5 x 0.5

x = 2.5 m

h = 5 - 2.5 = 2.5 m

using conservation of energy

mechanical energy is converted into kinetic energy

`M g h = (1)/(2)(M)v^2`

`v = √(2gh)`

`v = √(2* 9.8 * 2.5)`

v = 7 m/s

total energy when Jane leaves

Total energy =
`(1)/(2)Mv^2- (1)/(2)mv^2`

Total energy =
`(1)/(2)* 130 * 7^2- (1)/(2)* 50 * 7^2`

Total energy =1960 J

now,

maximum height attain by the Tarzan

m' g h' = total energy

80 x 9.8 x h' = 1960

h' = 2.5 m