Question

A 69.0kg diver is a height 2.70m above the water falling with a velocity 5.80m/s. Calculate her kinetic energy as she hits the water.

Answer 1

1372.26 Joules

Step-by-step explanation

Kinetic energy is the energy that an object possesses due to its motion, it is given by:

`\begin{gathered} KE=(1)/(2)mv^2 \\ \text{where m is the mass of the object} \\ v\text{ is the velocity of the object} \end{gathered}`

Potential energy is the stored energy an object has because of its position,it can be calculated using:

`\begin{gathered} PE=\text{mgh} \\ \text{where m is the mass of the object} \\ g\text{ is the acceleration due to gravity} \\ h\text{ is the heigth (position)} \end{gathered}`

The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another, so if we ignore the air resitance, we know the energy at A must be equal at the energy at B

so

`\begin{gathered} KE_A+PE_A=KE_B++PE_B \\ \text{replace} \\ (1)/(2)(m)(v_1)^2+(m)(g)(h)=(1)/(2)(m)(v_2)^2+(m)(g)(h) \\ (1)/(2)(69kg)(5.8(m)/(s)_{})^2+(8kg)(9.8(m)/(s^2))(2.7)=(1)/(2)(m)(v_2)^2+(8kg)(9.8(m)/(s^2))(0) \\ 1160.58+211.68=(1)/(2)(8)(v_2)^2+0 \\ 1372.26=4(v_2)^2 \\ \text{divide both sides by 4} \\ (1372.26)/(4)=(4(v_2)^2)/(4) \\ 343.065=(v_2)^2 \\ \text{square root in both sides} \\ √(343.065)=√((v_2)^2) \\ 18.52=v_B \end{gathered}`

therefore, the kinetick energy would be

`\begin{gathered} KE=(1)/(2)mv_b^2_{} \\ KE=(1)/(2)(8\text{ kg)}\cdot(18.52(m)/(s^2))^2 \\ KE=1372.26\text{ Joules} \end{gathered}`

so, the answer is

1372.26 Joules

I hope this helps you