Question

A woman is running around a playground while keeping an eye on her child who is on a swing set. The child is going back and forth one second per cycle of swinging. (a) What is the total distance run by the mother in five minutes if she has been going 5.0 m/s? (b) What is the total distance traveled by the child if the radius of the swing is 3.0 m and each swing covers a quarter of the circle?+

Answer 1

(a) 1500 m

(b) 2827.43m

Step-by-step explanation:

Given that the time for one cycle of the swing is 1 s

The radius of the swing, R= 3.0m

The angle covered, \theta, by each swing is a quarter of the circle. i.e.

`\Theta=\frac {\pi}{2}`

Speed of running of women =5 m/s.

Time of running = 5 minutes= 5 x 60 secondes= 300 s.

(a) As distance= (speed) x (time)

So, the required distance= 5 x 300 m= 1500 m.

(b) As there are two swings in one cycle, so, the distance covered in one swing is the length of the circular shown in the figure.

As arc length,
`l= \theta R`, where \theta is the angle, in radian, subtended by the arc at the center, and R is the radius of curvature of the arc.

So, the distance covered by the child in 1 swing
`= \frac {\pi}{2}* 3 m=(3\pi)/(2)m`.

In 1 cycle, there are 2 swings, so distance covered in 1 cycle
`= 3 \pi m`.

Now, in 1 second there is 1 cycle, so in 5 minutes there will be 300 cycles.

So, the total distance covered by the child

`= 3\pi* 300 m= 2827.43 m`.