Question

A 15.0 kg monkey starts to climb a long rope to reach a banana located at a height of 6.80 m. The rope will snap if the tension exceeds 165.00 N. Calculate the least amount of time the monkey could take to reach the banana without breaking the rope.

Answer 1

3.38061 seconds

Step-by-step explanation:

m = Mass of monkey = 15 kg

g = Acceleration due to gravity = 9.81 m/s²

a = Acceleration

u = Initial velocity

s = Displacement = 6.8 m

t = Time taken

The tension is given by

`T=m(g+a)\\\Rightarrow a=(T-mg)/(m)\\\Rightarrow a=(165-15* 9.81)/(15)\\\Rightarrow a=1.19\ m/s^2`

From equation of linear motion

`s=ut+(1)/(2)at^2\\\Rightarrow 6.8=0t+(1)/(2)* 1.19* t^2\\\Rightarrow t=\sqrt{(6.8* 2)/(1.19)}\\\Rightarrow t=3.38061\ s`

The time taken to reach the banana without breaking the rope is 3.38061 seconds