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Two trucks A and B travelling at 26km/hr and 28km/hr respectively approach one another on a straight road. Truck A is 10m long, while truck B is 15m long. Determine the time in seconds that elapse before the trucks completely pass each other (3 marks)

Mathematics

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Answer

53 sekunde\frac{5}{3} \text{ sekunde}

Step-by-step solution

4 steps

15) Muda wa Kupita Kabisa

  1. Tafuta kasi ya jamaa (relative speed) ya malori.

    Malori yanakaribiana, kwa hivyo kasi zao huongezwa pamoja ili kupata kasi ya jamaa.
    Kasi ya lori A (vAv_A) = 26 km/hr
    Kasi ya lori B (vBv_B) = 28 km/hr
    Kasi ya jamaa (vrelv_{rel}) = vA+vB=26 km/hr+28 km/hr=54 km/hrv_A + v_B = 26 \text{ km/hr} + 28 \text{ km/hr} = 54 \text{ km/hr}

  2. Badilisha kasi ya jamaa kuwa mita kwa sekunde (m/s).

    Ili kubadilisha km/hr kuwa m/s, zidisha kwa 10003600\frac{1000}{3600} au 518\frac{5}{18}.

    vrel=54 km/hr×1000 m3600 sv_{rel} = 54 \text{ km/hr} \times \frac{1000 \text{ m}}{3600 \text{ s}} vrel=54×518 m/sv_{rel} = 54 \times \frac{5}{18} \text{ m/s} vrel=3×5 m/sv_{rel} = 3 \times 5 \text{ m/s} vrel=15 m/sv_{rel} = 15 \text{ m/s}
  3. Tafuta umbali kamili unaohitajika kupitana.

    Ili malori yapitane kabisa, umbali wa jumla unaopaswa kufunikwa ni jumla ya urefu wao.
    Urefu wa lori A (LAL_A) = 10 m
    Urefu wa lori B (LBL_B) = 15 m
    Umbali wa jumla (DD) = LA+LB=10 m+15 m=25 mL_A + L_B = 10 \text{ m} + 15 \text{ m} = 25 \text{ m}

  4. Hesabu muda unaohitajika.

    Muda (tt) = Umbali / Kasi ya Jamaa

    t=Dvrelt = \frac{D}{v_{rel}} t=25 m15 m/st = \frac{25 \text{ m}}{15 \text{ m/s}} t=53 st = \frac{5}{3} \text{ s}

    Muda unaohitajika ni 53 sekunde\frac{5}{3} \text{ sekunde}.

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