Now
[tex]\\ \sf\longmapsto h=ut+\dfrac{1}{2}gt^2[/tex]
[tex]\\ \sf\longmapsto h=0t+\dfrac{1}{2}10t^2[/tex]
[tex]\\ \sf\longmapsto 500=5t^2[/tex]
[tex]\\ \sf\longmapsto t^2=100[/tex]
[tex]\\ \sf\longmapsto t=10s[/tex]
Now
[tex]\\ \sf\longmapsto h=cT[/tex]
[tex]\\ \sf\longmapsto T=\dfrac{h}{c}[/tex]
[tex]\\ \sf\longmapsto T=\dfrac{500}{340}[/tex]
[tex]\\ \sf\longmapsto T=1.47\approx 1.5s[/tex]
Total time:-
[tex]\\ \sf\longmapsto T_{net}=t+T=10+1.5=11.5s[/tex]
The total time of motion of the stone is 11.47 seconds.
The time taken for the stone to drop from the given height is calculated as follows;
[tex]h = v_0t + \frac{1}{2} gt^2\\\\h = 0 + \frac{1}{2} gt^2\\\\t = \sqrt{\frac{2h}{g} } \\\\t = \sqrt{\frac{2\times 500}{10} } \\\\t = 10 \ s[/tex]
The time it takes the stone to travel through the water is calculated as follows;
[tex]t = \frac{500}{340} \\\\t = 1.47 \ s[/tex]
Thus, the total time of motion of the stone is 1.47 + 10 = 11.47 seconds.
Learn more about time of motion here: https://brainly.com/question/2364404
