Subtopic: Functional requirements, principles of working, construction and operation of manual, animal, tractor and renewable energy operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing
Question Statement:
A seed planter travels forward at a constant speed of $v_f = 7.2\text{ km/h}$. A seed is released from the metering mechanism and drops freely through a vertical seed tube of height $h = 0.45\text{ m}$ into the open furrow. Assuming zero air drag, zero initial horizontal velocity relative to the planter ($v_{x0} = v_f$), and $g = 9.81\text{ m/s}^2$, the horizontal distance traveled by the seed relative to the ground during its fall inside the tube in $\text{cm}$ is ________ (round off to 1 decimal place).
Answer Key:
60.6
Step-by-Step Solution & Explanation
```
Seed Fall Kinematics:
v_f --->
[Metering Cup]
| \
| \ Parabolic Path
h = 0.45 m \
| \
v======o (Furrow floor)
|<-- x -->|
```
**Step-by-step Calculation:**
1. Forward speed of planter in $\text{m/s}$:
$v_f = \frac{7.2 \times 1000}{3600} = 2.0\text{ m/s}$
2. Free fall time $t$ for vertical drop height $h = 0.45\text{ m}$:
$h = \frac{1}{2} g t^2 \implies t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 0.45}{9.81}} = \sqrt{\frac{0.90}{9.81}} = \sqrt{0.09174} = 0.30289\text{ s}$
3. Horizontal displacement relative to the ground:
$x = v_f \times t = 2.0\text{ m/s} \times 0.30289\text{ s} = 0.60579\text{ m} = 60.58\text{ cm} \approx 60.6\text{ cm}$