In frozen Minnesota the winter sports carnival includes some unusual events. Since it is dangerous to run on ice, each runner runs on a heavy (240 kg) and long (40 m) wooden plank, which itself rests on the smooth and horizontal ice. One of the competitors is a 60 kg woman who runs the length of the plank in 4.4 seconds, quite an impressive time. Her performance is viewed by a crowd huddled on the ice. The performance that they see is less impressive. With what speed do they see her moving?

Question

In frozen Minnesota the winter sports carnival includes some unusual events. Since it is dangerous to run on ice, each runner runs on a heavy (240 kg) and long (40 m) wooden plank, which itself rests on the smooth and horizontal ice. One of the competitors is a 60 kg woman who runs the length of the plank in 4.4 seconds, quite an impressive time. Her performance is viewed by a crowd huddled on the ice. The performance that they see is less impressive. With what speed do they see her moving?

Answer 1

consider the log.

the log has to be moving at 60/240 *40/4.4 meters/sec=10/4.5

Consider relativity:
speed runner relative to observer=sr_o
speed runner relative to log=sr_log
speed log relative to observer=sl_o
sr_o=sr_log+sl_o
sr_o=40/4.4 + (-10/4.4)=30/4.4 m/s

Answer 2

To determine the speed at which the crowd sees the woman moving, we can use the concept of conservation of momentum. When a runner moves on a plank, the runner and the plank together form a system where the total momentum remains constant.

The total momentum can be calculated as the product of the mass and velocity of the runner-plank system before and after the run. Before the run, the system is at rest, so the initial momentum is zero. After the run, the system is still, as the woman stops at the end of the plank. Therefore, the final momentum is also zero.

Given that the woman has a mass of 60 kg and runs the length of the 40 m plank in 4.4 seconds, we can calculate her initial velocity using the equation:

Momentum = mass × velocity

Since the initial momentum is zero, we have:

0 = (60 kg + 240 kg) × initial velocity

Now we can solve for the initial velocity:

Initial velocity = 0 / (60 kg + 240 kg)
= 0 m/s

So, the woman does not move initially. However, we need to calculate the speed at which the crowd sees her. This can be determined based on the time it takes for the visual information to reach the crowd.

Since the woman takes 4.4 seconds to run the length of the plank, it takes a certain amount of time for the light to travel from the woman to the crowd. Therefore, the speed at which the crowd sees the woman is equal to the distance traveled (40 m) divided by the time it takes for the light to reach the crowd.

The speed seen by the crowd can be calculated as:

Speed seen by the crowd = Distance / Time

Speed seen by the crowd = 40 m / 4.4 s
= 9.09 m/s

Therefore, the speed at which the crowd sees the woman moving is 9.09 m/s.