Answer:
1.27551m
Explanation:
This is a simple energy convertion problem. Since there is no friction, and assuming no air drag and other external factors, mechanical energy should be conserved in this system.
Thus, we get:
[tex]KE_{initial} + PE_{initial} = KE_{final} + PE_{final}[/tex]
We also know that the gravitational potential energy is equal to mgh, while the KE can be calculated using [tex]\frac{1}{2}mv^2[/tex]
One thing to note here, is that the final KE will be 0, as there is no velocity at the end. Furthermore, we also can set the initial PE as 0 as we are looking at relative height, and at the start it is at h=0.
[tex]KE_{initial} = PE_{final}[/tex]
Plugging in:
[tex]\frac{1}{2}*30*5^2 = 30*9.8*h[/tex]
Solving for h, we get 1.27551m
