Classical Mechanics in Celeste - Golden Ridge

This shows the platformer game - Celeste , which has been very popular and high-ranked since last year. Now let's think of the Classical Mechanics based on it.

The image above shows the cloud, which can be seen attached to the spring whose spring constant is $k=800\ N/m$ . The cloud's mass is $m_1=6\ kg$ , and Madeline's mass is $m_2=42\ kg$ . Initially, Madeline stays rest along with the cloud. Suddenly, an upward wind force $F$ has been applied only to her, so that Madeline starts to move upwards with constant acceleration $a$ after $t=0$ . Before $t=0.4\ s$ , $F$ is gradually changing and after $0.4\ s$ , $F$ becomes constant.

Given these restrictions, and gravitational acceleration $g=10\ m/s^2$ , find:

• The constant acceleration $a$ .

• The minimum and maximum value of the wind force $F_{min}, F_{max}$ during the process.

Converting these data into SI units, and take the number part. Submit $\lfloor a+F_{min}+F_{max} \rfloor$ .

Assumptions:

• The cloud and Madeline both have gravity.

• Neglect air resistance.