Question

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.0 m long. His speed at the bottom of the swing is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 x 103 N. What is the largest mass that Tarzan can have and still make it safely across the river?

Answer 1

Answer:

61.73 kg

Explanation:

Maximum Tension, t = 1000 N

Let the mass of Tarzan is m.

Length of the rope, l = 10 m

velocity, v = 8 m/s

At the lowest point

T - mg = mv²/l

1000 - m x g = m x 64/10

1000 = m ( 9.8 + 6.4 )

m = 1000 / 16.2

m = 61.73 kg

Thus, the largest mass of Tarzan should be 61.73 kg.

Answer 2

Answer:61.72 kg

Explanation:

Given

Length of rope $L=10 m$

Speed at bottom of swing $v=8 m/s$

Breaking strength of string $T=1000 N$

At bottom Point

weight is acting downward and Tension is opposing it

Thus $T-mg=\frac{mv^2}{L}$

$T=mg+\frac{mv^2}{L}$

$1000=m(9.8+\frac{8^2}{10})$

$1000=m\cdot 16.2$

$m=61.72 kg$

maximum mass Tarzan can have is $61.72 kg$