Jeff of the jungle swings on a 7.6-m vine that initially makes an angle of 32 ∘ with the vertical.
if jeff starts at rest and has a mass of 83 kg , what is the tension in the vine at the lowest point of the swing?

To solve this problem we will use the trigonometric concepts to find the distance h, which will allow us to find the speed of Jeff and that will finally be the variable that will indicate the total tension, since it is the variable of the centrifugal Force given in the vine at the lowest poing of the swing.

From the image:

When Jeff reaches his lowest point his potential energy is converted to kinetic energy

Tension in the string at the lowest point is sum of weight of Jeff and the his centripetal force

Therefore the tension in the vine at the lowest point of the swing is 842.49N

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min