You are in an old spy movie and have been locked in a small room (V=1000 ft3 ). You suddenly realize that a poison gas has just started entering the room through a ventilation duct. Recognizing the type of poison from its smell, you know that if the gas reaches a concentration of 100 mg/m3 , you will die instantly, but that you are safe as long as the concentration is less than 100 mg/m3 . If the ventilation air flow rate in the room is 100 ft3 /min and the incoming gas concentration is 200 mg/m3 , how long do you have to escape? You may assume that the air in the small room is well-mixed.

no. dot product   =0 when vecs at right angles

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.