Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it’s not. After she sees that you have released the bill, it will take her about 0.25 s to react and close her fingers-which is not fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.

Question

ottcomn · Accepted Answer

Step 1  In this case the bill is doing a free fall.  Let, the distance traveled be denoted by s, the acceleration due to gravity be g , time taken to fall be t , and the initial velocity be denoted by u  Now, the given quantities:  s=16 cm  u=0 (as initially at rest)  g=9.8 m/s2  Apply the equation of motion to get,  s=ut+(12)gt2  Step 2  put the values, to get  16×10−2=12×9.8×t2  ⇒t2=2×16×10−29.8  ⇒t=0.18s  So, the time taken for the bill to fall beyond her grasp is 0.18s.  And as the average reaction time is 0.25s, so the friend would never catch it.

Jeffrey Jordon · Accepted Answer

The time taken by the bill to travel throught the fingers is,  s=12gt2  Here, g is acceleration due to gravity, t is time and s is length of the bill  t=2sg  =2(0.16m)9.8m/s2  =0.18s  Which is less than the reaction time (0.25 s)  of the person. So ,she cannot catch the bill  Therefore , the time taken by the bill to fall beyond her grasp is 0.18 s

Andre BalkonE · Accepted Answer

We can start by calculating the time it takes for the bill to fall a distance equal to the length of the bill, which is 16 cm. We can use the equation of motion for an object in free fall:s=12gt2where s is the distance fallen, g is the acceleration due to gravity, and t is the time taken.Since we are given the distance and we need to find the time, we rearrange the equation as follows:t=2sgThe acceleration due to gravity, g, is approximately 9.8m/s2. However, we need to convert the distance from centimeters to meters, so we divide the length of the bill by 100:t=2(0.16m)9.8m/s2Simplifying further:t=0.329.8sEvaluating the expression:t≈0.0327st≈0.181sTherefore, it takes approximately 0.181 seconds for the bill to fall beyond your friend&#039;s grasp.

Jazz Frenia · Accepted Answer

Let&#039;s first find the time it takes for the bill to fall a certain distance. We know that the length of the bill is 16 cm, which is equivalent to 0.16 m.Using the equation for free fall, we can find the time it takes for the bill to fall a certain distance (d) using the acceleration due to gravity (g):d=12gt2Solving for time (t):t=2dgPlugging in the values, with acceleration due to gravity approximately equal to 9.8m/s2:t=2×0.169.8Simplifying the equation:t=0.329.8t≈0.032653t≈0.1807sTherefore, it takes approximately 0.1807s for the bill to fall beyond your friend&#039;s grasp.

xleb123 · Accepted Answer

Result:0.18051Solution:We can use the equation of motion for the vertical direction:y=y0+v0t+12gt2where:- y is the vertical displacement (in meters) of the bill from its initial position- y0 is the initial vertical position of the bill (zero in this case)- v0 is the initial velocity of the bill (zero in this case)- t is the time (in seconds) for which the bill falls- g is the acceleration due to gravityThe vertical displacement y is equal to the length of the bill, which is 16 cm. We need to convert it to meters by dividing by 100:y=16100mSubstituting these values into the equation of motion, we get:16100=0+0·t+12·9.8·t2Simplifying the equation:16100=4.9t2Now we can solve for t. Dividing both sides of the equation by 4.9, we have:t2=16100·4.9Taking the square root of both sides:t=16100·4.9Evaluating the right-hand side of the equation:t≈0.032653s≈0.18051sTherefore, it takes approximately 0.18051 seconds for the bill to fall beyond your friend&#039;s grasp.

Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corne

Answered question

Answer & Explanation

New Questions in College Statistics