Arzan, who weighs 700 N, swings from a cliff at the end of a convenient vine thatis 20 m long. From the top of the cliff to the bottom of the swing, he descendsby 2.5 m. Unfortunately, at the bottom of his swing, the vine breaksand he fallsanother 5 m vertically. How far in the horizontal direction, d, does Tarzan travelfrom the point at which the vine breaks

= 7.07 m

Explanation:

The Tarzan reaches bottom of swing after descending 2.5 m,

change in his potential energy equals his kinetic energy at bottom of swing

m g h = (1/2) m v²   ,  

hence speed v of Tarzan at bottom of swing is given as  

v = ( 2 g h )1/2

= ( 2 × 9.8 × 2.5 )1/2

= 7 m/s

At the bottom of swing, if the vine breaks, then he is moving with horizontal velocity 7 m/s in gravitational field.  

If vertical distance from ground to bottom of swing is 5 m, then time t for Tarzan to reach ground is given by

S = (1/2)g t2 or   t = (2S/g)1/2

= ( 2 × 5 / 9.8 )1/2

= 1.01 s

Horizontal distance traveled by Tarzan = 1.01 × 7

= 7.07 m

that is probably false!