A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0° below the horizontal. The negligent driver leave

Question

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.82 m/s2 for a distance of 60.0 m to the edge of the cliff, which is 50.0 m above the ocean.

Required:
Find the car’s position relative to the base of the cliff when the car lands in the ocean.

in progress 0
Diễm Thu 3 years 2021-08-22T21:05:08+00:00 1 Answers 4 views 0

Answers ( )

    0
    2021-08-22T21:06:43+00:00

    Answer:

    The position is  P  =  47.4 \ m relative to the base of the ocean

    Explanation:

    From the question we are told that

        The angle made by the incline with the horizontal is \theta =  24.0 ^o

        The constant acceleration is a =  3.82 \ m/s^2

        The distance covered is d =  60.0 \ m

        The height of the cliff is h  =  50 .0 \ m

    The velocity of the car is mathematically represented as

          v^2 = u^2 +  2ad

    The initial velocity of the car is  u= 0

    So

         v^2 =  2ad

    substituting values

         v^2 = 2 *  3.82 * 60

        v =  21.4 \ m/s

    The vertical component of this velocity is

        v_v  =  -v * sin(\theta )

    substituting values

        v_v  = -21.4 * sin(24.0)

        v_v  = -8.7 \ m/s

    The negative sign is because is moving in the negative direction of the y-axis

    The horizontal  component of this velocity is

         v_h  =  v * cos (\theta)

        v_h  =  21.4 * cos (24.0)

        v_h  = 19.5 \ m/s

    Now according to equation of motion we have

         h  =  v_v*t  - \frac{1}{2} *  g t^2

    substituting  values

        50  =  -8.7 t  - \frac{1}{2} *  9.8 t^2

        4.9t^2  +8.7t -50 = 0

    using quadratic equation we have that

      t_1 = 2.42\ s \ and\   t_2 =  -4.20\ s

    given that time cannot be negative

          t = 2.42 \ s

    The  car’s position relative to the base of the cliff when the car lands in the ocean is mathematically evaluate as

               P  =  v_h * t

    substituting values

              P  =  19.5 *  2.43

             P  =  47.4 \ m

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )