44. Emily challenges her friend David to catch a dollar bill as follows. She holds the bill vertically, as in Figure P2.44, with the center of the bill between David’s index finger and thumb. David must catch the bill after Emily releases it without moving his hand downward. If his reaction time is 0.2 s, will he succeed? Explain your reasoning.
\(y_f=?\\y_o=0m\\a=-9.8m/s^2\\v_o=0m/s\)
\(y_f=y_o+v_ot+\frac{at^2}{2}\)
\(y_f=y_o+v_ot+\frac{at^2}{2}\)
\(y_f=-\frac{9.8m/s^2*t^2}{2}\)
At time t=0.2s;
\(y_f= 4.9m/s^2(0.2s)= -0.19=19 cm\)
He will not succeed, Because roughly half of a bill is 8cm and that's the maximum distance in order to catch the bill but as you can see the distance covered by the bill was 19cm, almost twice the distance of the half bill.
At time t=0.2s;
\(y_f= 4.9m/s^2(0.2s)= -0.19=19 cm\)
He will not succeed, Because roughly half of a bill is 8cm and that's the maximum distance in order to catch the bill but as you can see the distance covered by the bill was 19cm, almost twice the distance of the half bill.