Question

Bob drops a rock from the roof of a building (5m tall) onto Joe's head (1.5m tall). The mass of the rock is 0.5kg.a) What is the speed of the rock as it his Joe's head?b) If the rock is only travelling 8.0 m/s, how much work was done by air resistance?

Answer 1

Given:

The initial height of the rock was,

`h_i=5\text{ m}`

The final height of the rock is,

`h_f=1.5\text{ m}`

The mass of the rock is,

`m=0.5\text{ kg}`

The travelling speed of the rock is,

`v^(\prime)=8.0\text{ m/s}`

To find:

a) The speed of the rock at Joe's head

b) how much work was done by air resistance

Step-by-step explanation:

The displacement of the rock is,

`\begin{gathered} h=h_i-h_f \\ =5-1.5 \\ =3.5\text{ m} \end{gathered}`

The final speed at Joe's head is,

`\begin{gathered} v=√(u^2+2gh) \\ =√(0^2+2*9.8*3.5) \\ =√(68.6) \\ =8.28\text{ m/s} \end{gathered}`

Hence, the speed of the rock at Joe's head is 8.28 m/s.

b)

The speed at Joe's head was 8.0 m/s, and the loss of kinetic energy is,

`\begin{gathered} (1)/(2)* m[(8.23)^2-(8.0)^2] \\ =(1)/(2)*0.5*[3.73] \\ =0.93\text{ J} \end{gathered}`

This loss of energy is the work done by the air resistance.

Hence, the work done by the air resistance is 0.93 J.