Why is the following situation impossible? Emily challenges David to catch a $1 bill as follows. She holds the bill vertically with the center of the bill between, but not touching David’s index finger and thumb. Without warning, Emily releases the bill. David catches the bill without moving his hand down- ward. David’s reaction time is equal to the average human reaction time
David will be unsuccessful. The average human reaction time is about 0.2 s (research on the Internet) and a dollar bill is about 15.5 cm long, so David’s fingers are about 8 cm from the end of the bill before it is dropped. The
bill will fall about 20 cm before he can close his fingers
The situation described is impossible because of the law of gravity. When Emily releases the bill without warning, it will fall downward due to the gravitational force acting on it. David's reaction time, no matter how fast it is, cannot counteract the force of gravity and prevent the bill from falling downward. In order to catch the bill, David would need to move his hand downward to intercept its path.
The situation described is impossible because of the principles of physics and human reaction time.
When Emily releases the bill without warning, it starts falling due to gravity. David's reaction time, which is equal to the average human reaction time, refers to the time it takes for him to realize that the bill is falling and initiate a response.
However, even with an immediate reaction, it would still take some amount of time for David to physically move his hand downward to catch the falling bill. During this time, the bill would continue to fall freely, and David's hand would not be able to reach it quickly enough without moving downward.
This is because the force of gravity accelerates the bill downwards, and it will gain speed as it falls. On the other hand, David's reaction time and physical movement to catch the bill are limited by the capabilities of the human body and its reaction time.
To catch the falling bill, David would need to move his hand downward faster than the bill is falling. However, this requires predicting when the bill will be released and starting the downward movement before Emily actually releases it. Since the release is described as without warning, David would not have enough time to react and catch the bill without moving his hand downward.
In summary, the situation is impossible because human reaction time and the physical limitations of the human body prevent David from catching a falling bill without moving his hand downward.