Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.4 m long. his speed at the bottom of the swing, just as he clears the surface of the river, is 8.5 m/s. tarzan does not know that the vine has a breaking strength of 1.4 × 103 n. the acceleration of gravity is 9.81 m/s 2 . what is the largest mass tarzan can have and make it safely across the river? answer in units of kg.

83.5 kg

Explanation:

from the question we are given the following :

length of the vine (r) = 10.4 m

velocity (v) = 8.5 m/s^{2}

breaking strength of the vine (T) =1.4 x 10^{3} N

acceleration due to gravity (g) = 9.81 m/s^{2}

maximum mass (m) = ?

we can get the maximum mass by applying the equation below

ΣF = ma

where      

ΣF = Tension (breaking strength) - ( mass x acceleration due to gravity)

ma = mass x acceleration = mass x

1400 - (m x 9.81) = m × \frac{8.5^{2}}{10.4}

1400 - 9.81 m = 6.95 m

1400 = 6.95 m + 9.81 m

1400 = 16.76 m

m = 83.5 kg