Answer:
[tex]|D_{depth} |=19.697m[/tex]
Explanation:
To find Depth D of lake we must need to find the time taken to hit the water.So we use equation of simple motion as:
Δx=vit+(1/2)at²
[tex]x_{f}-x_{i}=v_{i}t+(1/2)at^{2}\\ -5.0m=(o)t+(1/2)(-9.8m/s^{2} )t^{2}\\ -4.9t^{2}=-5.0\\ t^{2}=5/4.9\\t=\sqrt{1.02} \\t=1.01s[/tex]
As we have find the time taken now we need to find the final velocity vf from below equation as
[tex]v_{f}=v_{i}+at\\v_{f}=0+(-9.8m/s^{2} )(1.01s) \\v_{f}=-9.898m/s[/tex]
So the depth of lake is given by:
first we need to find total time as
t=3.0-1.01 =1.99 s
[tex]|D_{depth} |=|vt|\\|D_{depth} |=|(-9.898m/s)(1.99s)|\\|D_{depth} |=19.697m[/tex]
