Question

A dart player throws a dart horizontally at a speed of 12.4 m/s. The dart hits the board 0.32 m below the height from which it was thrown. How long does it take the dart to hit the board? Round your answer to the nearest hundredth of a second (before square rooting, keep 4 places past the decimal point)

Answer 1

Step-by-step explanation:

It is given that,

The horizontal speed of a dart player = 12.4 m/s

The dart hits the board 0.32 m below the height from which it was thrown.

We need to find how long it take the dart to hit the board.

Let the time taken by the dart to hit the board. Using second equation of motion to find it.

`y=ut+(1)/(2)at^2\\\\\text{Put u = 0 and a= -g}\\\\y=(-1)/(2)gt^2\\\\-0.32=(-1)/(2)* 9.8t^2\\\\t=\sqrt{(2* 0.32)/(9.8)}\\\\t=0.255\ s`

Let x be the horizontal distance travelled. It is calculated as follows :

`x=12.4* 0.255\\\\=3.16\ m`

So, the dart will hit the board at a distance of 3.16 m.