Question

A $50kg$ acrobat is swinging on a rope with a length of $15m$ from one horizontal platform to another. Both platforms are at equal height.
If the maximum tension the rope can support is $1200N$, which of the following answer best represents the maximum velocity the acrobat can reach without breaking the rope?

• A. $25m/s$
• B. $19m/s$
• C. $20m/s$
• D. $15m/s$
• E. $5m/s$

Answer 1

Answer: (D)

$15m/s$

Given : $T=1200$ N $m=50$ kg $L=15$ m

Let the maximum velocity of the acrobat be $v$.

From figure, $\frac{m{v}^2}{L}=T-mg$

$\therefore$ $\frac{50\times v^2}{15}=1200-50\times 9.8$ $⟹v=\sqrt{213}\approx 15$ $m/s$