Question

A runner is jogging in a straight line at a steady Vr= 3.4km/hr. When the runner is L=8km from the finish line, a bird begins flying straight from the runner to the finish line at Vb= 17km/hr(5 times as fast as the runner). When the bird reaches the finish line, it turns around and flies directly back to the runner. What cumulative distance does the bird travel?

Answer 1

The cumulative distance that the bird travel is 13.33 Km

Step-by-step explanation:

Given that,

Velocity of runner = 3.4 km/hr

Distance = 8 km

Velocity of bird = 17 km/hr

Let x is the distance from the origin where the runner run into the bird

We need to calculate the value of x

Using time of runner and bird

`t_(r)=t_(b)`

`(d_(r))/(v_(r))=(d_(b))/(v_(b))`

Put the value into the formula

`(x)/(3.4)=(8+(8-x))/(17)`

`17x=3.4*8+3.4(8-x)`

`17x=27.2+27.2-3.4x`

`17x+3.4x=54.4`

`x=(54.4)/(20.4)`

`x=2.67`

We need to calculate the cumulative distance that the bird travel

Using distance of bird

`d_(b)=16-x`

Put the value into the formula

`d_(b)=16-2.67`

`d_(b)=13.33\ km`

Hence, The cumulative distance that the bird travel is 13.33 Km