The three forces acting on a hot-air balloon that is moving vertically are its weight, the force due to air resistance and the upthrust force. the hot-air balloon descends vertically at constant speed. the force of air resistance on the balloon is f. which weight of material must be released from the balloon so that it ascends vertically at the same constant speed? a f b 2f c 3f d 4f

Explanation :

The forces acting on hot- air balloon are:

Weight, (W)

Force due to air resistance, (F)

Upthrust force, (U)

Its weight W is acting in downward direction. The upthrust force U acts in upward direction. When the balloon is moving upward, the air resistance is in downward and vice versa.

In this case, the hot-air balloon descends vertically at constant speed.

so,

and

so, ....................(1)

when it is ascending let the weight that it is releasing is R, so

..........(2)

solving equation (1) and (2)

2F is the weight of material that must be released from the balloon so that it ascends vertically at the same constant speed.

b

explanation:

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.