A hot air balloon is descending with a velocity of 2.0 m/s straight down. At a height of 6m, a champagne bottle is opened to celebrate a successful flight, expelling the cork horizontally with a velocity of 5.0 m/s. a. What is the initial velocity (magnitude and direction) of the cork, as seen by an observer on the ground? b. What are the horizontal and vertical components of the initial velocity? c. How long is the cork in the air? d. How far away from the balloon does it land?

a

b

Horizontal component

vertical component

c

d

Explanation:

Generally from the question we can deduce that he initial velocity of the cork, as seen by an observer on the ground in terms of the x  unit vector is  

      due to the fact that the cork is moving horizontally

Generally from the question we can deduce that the vertical and horizontal  components of the initial velocity is  

        due to the fact that the balloon is moving downward which is the negative which will also cause the cork to move vertically with the balloon speed

Generally the  initial velocity (magnitude and direction) of the cork, as seen by an observer on the ground is mathematically represented as

Generally the  initial direction of motion as seen by the same observer is mathematically represented as

Generally the time taken by the cork in the air before landing is mathematically represented as

So  D =  6 \  m from the question

     g =  9.8 \  m/s^2

     u  =   =  2 m/s  this because we are considering the  vertical motion

So

Solving using quadratic formula w have that

Generally the distance of the cork from the balloon is mathematically represented as

multiple

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.