using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.



Answer :

Using energy considerations Since Ef=Ei, a rock thrown from the tip of a bridge doesn't matter which direction it is thrown in.

Given that,

Height of the bridge is 20m

Initial before he throws the rock

The height is hi = 20 m

Then, final height hitting the water

hf = 0 m

Initial speed the rock is throw

Vi = 15m/s

The speed at final is at which the rock hits the water

Vf = 24.8 m/s

Using given energy conservation

Ki + Ui = Kf + Uf

Where

Ki is initial kinetic energy

Ui is initial potential energy

Kf is final kinetic energy

Uf is final potential energy

Then,

Ki + Ui = Kf + Uf

Where

Ei = Ki + Ui

Where Ei is initial energy

E i =1/2mVi² +m*g*hi

E i =1/2m × 15² + m *9.8*20

E i = 112.5m + 196m

E i = 308.5m J

Now,

E f = Kf + Uf

E f =1/2mVf² + m*g*hf

E f =1/2m*24.8² + m*9.8* 0

E f = 307.52m + 0

E f = 307.52m J

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