Question 1

Your friend needs some help from you for creating a circuit without the use of any micro-controllers (can use simple ICs and basic electronic components).

Whenever an obstacle is in a vicinity of 30 cm of HC-SR04 sensor, run a motor for 5s and then stop.
The motor should only be retriggered when the existing obstacle is moved away from the vicinity of 30cm and re-enter the 30 cm range.

Method 1

Possible steps

Find a way to measure distance using HC-SR04 sensor from it datasheet
make a circuit that can replicate the process without using a micro-controller like Arduino

Actual Step

Make a triggering circtuit that will trigger the HC-SR04

The pulse should be greater than $10 u s$

Make a Mono-Stable Multi-Vibrator using SE555 timer
Requirements
- $5 S e c$ $T_{o n}$
- Differentiator with $f_{c} = inverse T of the ECHO Out$

Astable Multi-Vibrator Design

Design

Choosing $T = 1 S e c$
Choosing

Mono-Stable Multi-Vibrator Design

Requirements:
$T_{o n} = 5 s e c$

\begin{aligned} We know \\ T & = 1.1 R C \\ 5 & = 1.1 R C \\ R & = \frac{5}{1.1 C} \\ let C = 0.1 µ F \\ R & = 45454545 Ω & = 45 M Ω \\ By choosing higher value of C \\ let C = 100 µ F \\ R & = \frac{5}{1.1 \times 100 \times 10^{- 6}} \\ = 45.454 K Ω \end{aligned}

Differentiator -> HPF Circuit

Requirements: The HC-SR04 produces a $1.740 m s$ pulse when the target is near $30 c m$

So the $T o n$ will be $1.740 m s$

We can have any frequency but it should satisfy some condition like $T_{o n} = 1.74 m s$ so the best possible frequency is $\frac{1}{2 m s} = 500 H z$

Design

We Know

\begin{aligned} R_{1} C_{1} & \leq 0.0016 T_{t} \end{aligned}

let $C_{1} = 0.01 μ F$

\begin{aligned} ∴ R_{1} \times 0.01 \times 10^{- 6} & \leq 0.0016 T_{t} \end{aligned}

We know $T_{t} = 1.74 m s$

\begin{aligned} R_{1} & = \frac{0.0016 \times 1.74 \times 10^{- 3}}{0.01 \times 10^{- 6}} \\ = 278.4 Ω \end{aligned}

Designing a Duty Cycle Detector

In this i will use the theory that capacitor will take some time to charge which can be utilized get to the $T_{o n}$ of a certain frequency