Question

A girl is sledding down a slope that is inclined at 30.08 with respect to the horizontal. The wind is aiding the motion by providing a steady force of 105 N that is parallel to the motion of the sled. The combined mass of the girl and the sled is 65.0 kg, and the coeffi cient of kinetic friction between the snow and the runners of the sled is 0.150. How much time is required for the sled to travel down a 175-m slope, starting from rest?

Answer 1

Answer:t=8.16 s

Step-by-step explanation:

Given

`\theta =30.8`

Steady Force
`\left ( F\right )=105 N`

Friction force
`\left ( f\right )=0.15* 65* 9.81* cos\left ( 30.08\right )`

f=82.766 N

Using FBD

`F+mgsin\theta -f=ma`

`105+65* 9.81* sin\left ( 30.08\right )-82.766=65\left ( a\right )`

`105+319.6-82.766=65\left ( a\right )`

`a=5.25 m/s^2`

time to reach bottom

`s=ut+(1)/(2)at^2`

`175=0\left ( t\right )+(1)/(2)\left ( 5.25\right )t^2`

`t^2=66.667`

t=8.164 sec