Conservation of mechanical energy ?

[XxphysicsxX]

Conservation of mechanical energy ?

A 0.80kg coconut is growing 10m above the ground in its palm tree. The tree is just at the edge of a cliff that is 15 meters tall.

a>What would the maximum speed of the coconut be if it fell to theground beneath the tree?
b>What would the maximum speed be if it fell from the tree to the bottom of the cliff?

Equations:
Ep=mgh
Ek= -Ep
Ek= (1/2)mv^2

The Attempt at a Solution

So I've figured out Ep= 78.48J
However,Im not sure how to relate that to Ek so I could later solve for v?

 

[Sourabh N]

The second relation you wrote, relates Ek to Ep. Also notice that Ep would be -78.48 J (why?)

 

[XxphysicsxX]

so for a>
Ep= -78.48J so Ek= 78.48J
Ek= (1/2)(0.80kg)v^2
v= 14.0 m/s

is that right??

 

[Sourabh N]

Yes. For second part, the height changes (to?)

 

[XxphysicsxX]

for b>
Ep= (.80)(9.81)(25cm)
Ek= 196.2J
196.2/ 0.4 = v^2
v= 22.14m/s

 

[Sourabh N]

That looks good.

Edit : I assumed you meant 25m and not 25 cm.

 

[XxphysicsxX]

Oops yes, I meant 25m.
Thank you! :)

 

[Sourabh N]

You are welcome!