Question

A monkey is swinging from a tree. On the first swing, she passes through an arc of
20
m
20 m20, start text, space, m, end text. With each swing, she passes through an arc
4
5
5
4
​
start fraction, 4, divided by, 5, end fraction the length of the previous swing.

Answer 1

Answer:

Approximately 90 m.

Step-by-step explanation:

Given :

Length of the arc in initial swing = 20m

So, the drop after every swing is 4/5 of previous swing .

or, Dn+1 = 4/5 of Dn

so, D2 = 4/5 of 20 = 16 m

D3 = 4/5 of 16 = 4/5 x 4/5x20 = (4/5)²x 20

D4 = 4/5 of D3 = 4/5 x 4/5 x 4/5 x 20 = (4/5)³ x 20

.

.

so, Dn+1 = (4/5)^n x 20

.

so, D10 = 4/5 of D9 = (4/5)^9 x 20

Adding All the distances, we get

D1 + D2 + ......D10

= 20 + 4/5x20 + (4/5)²x20 + ..........+ (4/5)^9x20

= 20[ 1 + 4/5 + (4/5)² + (4/5)³ + ....+ (4/5)^9 ]

Now we got GP with a1 = 1, r = 4/5 and n = 10

So, Formula for the sum of n terms of GP

We get, Sn = 4.4631

So, Total distance travelled by monkey in 10 swings

is 20xSn

= 89.765 m