Question

A 7.51kg rock is dropped from the top of a 4.5m high bridge. How fast will the rock be traveling as it hits the water if we ignore air resistance

Answer 1

Given that the mass of the rock is, m = 7.51 kg

The height of the bridge is, h = 4.5 m

The potential energy of the rock is

`P\mathrm{}E\text{. =mgh}`

Here, the acceleration due to gravity, g = 9.8 m/s^2

Substituting the values, the potential energy will be

`\begin{gathered} P\mathrm{}E\mathrm{}=7.51*9.8*4.5 \\ =331.191\text{ J} \end{gathered}`

The potential energy will be converted to kinetic energy

`PE\text{ = K E}`

Also, Kinetic energy will be

`\begin{gathered} KE\text{ = }(1)/(2)mv^2 \\ v=\sqrt[]{(2KE)/(m)} \end{gathered}`

Here, v is the speed of the rock.

Substituting the values, the speed of the rock will be

`\begin{gathered} v=\sqrt[]{(2*331.191)/(7.51)} \\ =\sqrt[]{88.2} \\ =9.391\text{ m/s} \end{gathered}`

The speed of the rock will be 9.391 m/s