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postnew [5]
1 year ago
13

If the swimmer starts at rest, slides without friction, and descends through a vertical height of 2.41 m

Physics
1 answer:
AveGali [126]1 year ago
7 0

Answer:

6.88 m/s

Explanation:

The Conservation of Energy states that:

Initial Kinetic Energy + Initial Potential Energy = Final Kinetic Energy + Final Potential Energy

So we can write

mgh_{i}+\frac{1}{2}mv_{i} ^{2}=mgh_{f}+\frac{1}{2}mv_{f} ^{2}

We can cancel the common factor of m which leaves us with

gh_{i}+\frac{1}{2}v_{i} ^{2}=gh_{f}+\frac{1}{2}v_{f} ^{2}

Lets solve for v_f

gh_{i}+\frac{v_{i} ^{2}}{2}=gh_{f}+\frac{v_{f} ^{2}}{2}

Subtract gh_f from both sides of the equation.

gh_{i}+\frac{v_{i} ^{2}}{2}-gh_{f}=\frac{v_{f} ^{2}}{2}

Multiply both sides of the equation by 2.

2(gh_{i}+\frac{v_{i} ^{2}}{2}-gh_{f})={v_{f} ^{2}

Simplify the left side.

Apply the distributive property.

2(gh_{i})+2\frac{v_{i} ^{2}}{2}+2(-gh_{f})={v_{f} ^{2}

Cancel the common factor of 2.

2gh_{i}+v_{i} ^{2}-2gh_{f}={v_{f} ^{2}

Take the square root of both sides of the equation to eliminate the exponent on the right side.

{v_{f}=\sqrt{2gh_{i}+v_{i} ^{2}-2gh_{f}}

We are given g,v_{i},h_{i},h_{f}.

We can now solve for the final velocity.

{v_{f}=\sqrt{(2*9.81*2.41)+(0^{2})-(2*9.81*0)

Anything multiplied by 0 is 0.

{v_{f}=\sqrt{2*9.81*2.41

{v_{f}=\sqrt{47.2842

v_f=6.88

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