Question

In Fig 2-22, a cream tangerine is thrown directly upward past three evenly spaced windows of equal heights. Rank the windows according to (a) the average speed of the cream tangerine while passing them (b) the time the cream tangerine takes to pass them, (c) the magnitude of the acceleration of cream tangerine while passing them and (d) the changein the speed of cream tangerine during the passage, greatest first.

Short answer

(a) The descending order of windows according to the average speed of the cream tangerine while passing them is as,3,2,1

(b) The descending order of windows according to the time the cream tangerine takes while passing them is as, 1,,2,3

(c) The descending order of windows according to the acceleration of the cream tangerine while passing them is as, the acceleration while passing all windows is the same.

(d) The descending order of windows according to the change in the speed of the cream tangerine while passing them is as, 1,2,3

Step-by-step solution

Given information

Evenly spaced windows in figure 2.22.

Constant Acceleration

The problem deals with the constant acceleration which is the rate of change of velocity with respect to time. When the velocity of an object changes at a constant rate, this rate is called constant acceleration.

(a) To rank the windows according to the average speed

As an object moves upwards, its speed goes on decreasing. This means the distance covered in unit time goes on decreasing. So, the descending order of windows according to the average speed of the cream tangerine while passing them is 3,2,1 .

(b) To rank the windows according to the time

As an object moves upwards, its speed goes on decreasing. This means the time required to cover a unit distance goes on increasing. So, the descending order of windows according to the time the cream tangerine takes while passing them is 1,2,3

(c) To rank the windows according to the magnitude of the acceleration

The only force acting on the tangerine is the force due to gravity (neglecting air resistance). So, its acceleration is constant, equal to -g. Thus, the acceleration while passing all windows is the same.

(d) To rank the windows according to the change in speed ∆v

$v=a∆t$In this case, a is constant and equal to –g. As the tangerine moves upwards, its speed goes on decreasing, and the time required to cover a unit distance goes on increasing. The descending order of windows according to the change in the speed of the cream tangerine while passing them is then 1,2,3 .