Explanation:
The formula to calculate total time taken is as follows.
Total time = time to fall + time for sound
So, time for sound = [tex]\frac{distance}{velocity}[/tex]
= [tex]\frac{7.03}{343}[/tex]
= 0.0204 sec
Hence, time to fall is as follows.
(0.81 - 0.0204) sec
= 0.7896 sec
Now, we will calculate the time to fall as follows.
y = [tex]y_{o} + v_{o}yt + \frac{1}{2}at^{2}[/tex]
0 = [tex]h + v \times t - \frac{1}{2}gt^{2}[/tex]
0 = [tex]7.03 + v \times (0.81 - 0.0204) - 0.5 \times 9.81 \times(0.81 - 0.0204)^{2}[/tex]
= [tex]7.8196 - 0.5 \times 9.81 \times 0.623[/tex]
= 7.8196 - 3.058
= 4.7616 m/s
Therefore, she threw the coin at 4.76 m/s in the upward direction.
