Emily challenges her husband, David, to catch a $1 bill as follows. She holds the bill vertically, with the center of the bill between David's index finger and thumb. David must catch the bill after Emily release it without moving his hand downward. If his reaction is 0.2 s, will he succeed? Explain your reasoning.

Question

Emily challenges her husband, David, to catch a $1 bill as follows. She holds the bill vertically, with the center of the bill between David's index finger and thumb. David must catch the bill after Emily release it without moving his hand downward. If his reaction is 0.2 s, will he succeed? Explain your reasoning.

Answer 1

The bill is about 7 cm. high.

So David has to catch it before it falls through 7cm, assuming David's fingers are right below Emily's.
Here,
g=-9.8 m/s²
S=-0.07m
initial velocity, u =0
S=ut+(1/2)gt²
Solve for t to see if it exceeds 0.2 s.

Answer 2

To determine if David will succeed in catching the bill, we need to compare his reaction time to the time it takes for the bill to fall.

Let's assume that the bill is released from rest and falls freely under gravity. The key point to note is that the bill starts at rest and only moves when released, meaning its initial velocity is zero.

To analyze the situation mathematically, we can use the equation for the distance an object falls under gravity:

d = 0.5 * g * t^2

where:
- d is the distance fallen
- g is the acceleration due to gravity (~9.8 m/s^2)
- t is the time fallen

We want to find the time it takes for the bill to fall when David's reaction time is 0.2 seconds.

Substituting the values into the equation:
d = 0.5 * 9.8 * (0.2)^2
d = 0.98 * 0.04
d = 0.0392 meters

Therefore, the bill will fall approximately 0.0392 meters during David's reaction time of 0.2 seconds.

Now, let's consider whether David will be able to catch the bill. If David's hand is located at a distance greater than 0.0392 meters below the initial position of the bill, then he will be able to catch it. However, if his hand is less than 0.0392 meters below the initial position, he will not be able to catch it without moving his hand downward.

Ultimately, the answer depends on the distance between David's hand and the initial vertical position of the bill when it is released. If this distance is less than 0.0392 meters, David will not be able to catch the bill without moving his hand downward within his reaction time.