Question

A runner is jogging in a straight line at a

steady vr= 8.4 km/hr. When the runner is

L= 6.3 km from the finish line, a bird begins

flying straight from the runner to the finish

line at vb= 42 km/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.

Answer 1

Total distance traveled by bird is 10.5 km.

Step-by-step explanation:

Given that,

Velocity of runner= 8.4 km/hr

Distance = 6.3 km

Velocity of bird = 42 km/hr

Suppose, How far does the bird travel?

We need to calculate the time of bird

Using formula of time

`t=(d)/(v_(b))`

Put the value into the formula

`t=(6.3)/(42)`

`t=0.15\ hr`

We need to calculate the distance runner travels during time period

Using formula of distance

`d=v_(r)* t`

`d=8.4*0.15`

`d=1.26\ km`

We need to calculate the distance of runner to FL

Using distance

`d'=6.3-1.26`

`d'=5.04\ km`

We need to calculate the net closing speed between runner and bird

Using speed

`v'=v_(r)+v_(b)`

`v'=8.4+42`

`v'=50.4\ km/hr`

We need to calculate the time for runner and bird to meet

Using formula of time

`t=(d)/(v')`

Put the value into the formula

`t=(5.04)/(50.4)`

`t=0.1\ hr`

We need to calculate the distance covered by runner

Using formula of distance

`d=vt`

Put the value into the formula

`d=8.4*0.1`

`d=0.84\ km`

We need to calculate the distance covered by bird to runner

Using formula of distance

`d=vt`

Put the value into the formula

`d=42*0.1`

`d=4.2\ km`

We need to calculate the total distance

Using distance

`D=6.3+4.2`

`D=10.5\ km`

Hence, Total distance traveled by bird is 10.5 km.