Question

Marbles are exiting a container through a horizontal nozzle positioned 1.3 m above sandy ground. You notice that all the marbles land between 0.23 m and 0.41 m from the point directly below the end of the nozzle. What is the minimum initial speed of the marbles?

Answer 1

The minimum initial speed of the marbles are 2.6 m/s

Step-by-step explanation:

Given that,

Height = 1.3 m

For vertical displacement,

We need to calculate the time

Using equation of motion

`s=ut+(1)/(2)gt^2`

Put the value into the formula

`1.3=(1)/(2)*9.8t^2`

`t=\sqrt{(2*1.3)/(9.8)}`

`t=0.51\ sec`

We need to calculate the minimum initial speed of the marbles

Using formula of speed

`v=(d)/(t)`

Put the value into the formula

`v=(1.3)/(0.51)`

`v=2.6\ m/s`

Hence, The minimum initial speed of the marbles are 2.6 m/s