Question

In Fig. 4-25, a cream tangerine is thrown up past windows 1, 2, and 3, which are identical in size and regularly spaced vertically. Rank those three windows according to (a) the time the cream tangerine takes to pass them and (b) the average speed of the cream tangerine during the passage, greatest first. The cream tangerine then moves down past windows 4, 5, and 6, which are identical in size and irregularly spaced horizontally. Rank those three windows according to (c) the time the cream tangerine takes to pass them and (d) the average speed of the cream tangerine during the passage, greatest first.

Short answer

1. Rank : 3 > 2 > 1
2. Rank : 1 > 2 > 3
3. Rank : 1 = 2 = 3
4. Rank : 6 > 5 > 4

Step-by-step solution

Given information

• Windows 1, 2 and 3: regularly spaced vertically.
• Windows 4, 5 and 6: irregularly spaced horizontally.

To understand the concept

This problem is based on the concept of projectile motion. When a particle is thrown near the earth’s surface, it travels along a curved path under constant acceleration directed towards the center of the earth surface. Also, it deals with the kinematic equations of motion in which the motion can be described with constant acceleration. This problem can be solved by using the kinematic equations for two-dimensional motion:

horizontal motion with constant speed and vertical motion with acceleration due to gravity.

Formulae:

$$\begin{gathered} v_{fy}=y_{0y}-gt \\ ∆y=v_{0y}t-\left(\frac{1}{2}g{t}^2\right) \end{gathered}$$

(a) Rank windows 1, 2 and 3 according to time the cream tangerine takes to pass them

Since the acceleration is in the downward direction, velocity would decrease with height and hence time would increase,

Rank : 3 > 2 > 1

(b) Rank windows 1, 2 and 3 according to the average speed of tangerine during passage

$v_{fy}=v_{0y}-gt$

As time increases, average speed decreases.

Hence,

Rank : 1 > 2 > 3

(c) Rank windows 4, 5 and 6 according to the time the cream tangerine takes to pass them

To pass horizontally, time required will be same for each window because there is no acceleration due to horizontal motion.

Hence,

Rank : 1 = 2 = 3

(d) Rank windows 4, 5 and 6 according to the average speed of the cream tangerine during the passage.

During the movement in the direction of an acceleration speed is increasing with time.

Hence,

Rank : 6 > 5 > 4