Question

: A 70 kg man and a 12 kg sled are on the frictionless ice of a frozen lake, 25 m apart but connected by a rope of negligible mass. The man exerts a horizontal 8.2 N force on the rope. How long (in seconds) does it take from the man’s initial position until they meet?

Answer 1

`x_1 = 3.74m`

Step-by-step explanation:

given,

mass of man = 70 kg

mass of sled = 12 kg

F = m a_s

`a_s = (F)/(m)`

`a_s = (8.2)/(12)`

`a_s = 0.68\ m/s^2`

`F = m a_m`

`a_m = (F)/(m)`

`a_m = (8.2)/(70)`

`a_m = 0.12\ m/s^2`

`x_1+x_2 = 25`

`(1)/(2)a_ct^2+ (1)/(2)a_mt^2 = 25`

`(a_c+a_m)t^2=50`

`(0.12+0.68)t^2=50`

`t = \sqrt{(50)/(0.8)}`

t = 7.90 s

`x_1 = (1)/(2)a_ct^2`

`x_1 = 0.5* 0.12 * 7.90^2`

`x_1 = 3.74m`