Answer to Question #101946 in Mechanics | Relativity for dan

Question

kangaroos are good runners that can sustain a speed of 56 km/h (15.5 m/s). suppose a kangaroo is sitting on a log that is floating in a lake. when the kangaroo gets scared, she jumps off the log with a velocity of 15 m/s toward the bank. the log moves with a velocity of 3.8 m/s away from the bank. if the mass of the log is 250 kg, what is the mass of the kangaroo?

Answer 1

We can find the mass of the kangaroo from the Law of Conservation of Momentum. Let's choose the direrection toward the bank as the positive and apply the Law of Conservation of Momentum:

$$m_kv_{k,i} + m_{log}v_{log, i} = m_kv_{k,f} - m_{log}v_{log, f},$$

here, $m_k$ is the mass of kangaroo, $m_{log} = 250kg$ is the mass of the log, $v_{k, i} = 0 \dfrac{m}{s}$ is the initial velocity of the kangaroo, $v_{log, i} = 0 \dfrac{m}{s}$ is the initial velocity of the log, $v_{k,f} = 15 \dfrac{m}{s}$ is the final velocity of the kangaroo, $v_{log,f} = 3.8 \dfrac{m}{s}$ is the final velocity of the log.

Then, we get:

$$m_kv_{k,f} - m_{log}v_{log, f} = 0.$$

From this equation we can find the mass of the kangaroo:

$$m_{k} = \dfrac{m_{log}v_{log,f}}{v_{k,f}} = \dfrac{250kg \cdot 3.8 \dfrac{m}{s}}{15 \dfrac{m}{s}} = 63kg.$$

Answer:

$m_{k} = 63kg.$