The deck of a bridge is suspended 235 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble a

Question

The deck of a bridge is suspended 235 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 235 − 16t^2.

Required:
a. Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time.

1. 0.1 sec:________
2. 0.05 sec:_______
3. 0.01 sec:_______

b. Estimate the instantaneous velocity (in ft/s) of the pebble after 3 seconds. ft/s.

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Khánh Gia 4 years 2021-07-21T03:12:37+00:00 1 Answers 1028 views 1

Answers ( )

  1. Sigrid
    0
    2021-07-21T03:13:56+00:00
    Reply

    Answer:

    (a) 1, average velocity = -65.6 m/s

       2, average velocity = -64.8 m/s

       3, average velocity = -64.16 m/s

    (b) The instantaneous velocity is -96 m/s

    Explanation:

    (a)

    Average velocity is given  by;

    y(t_2,t_1) = \frac{y(t_2) - y(t_1)}{t_2-t_1}

    (1)

    y(2.1,2) = \frac{(235-16*2.1^2) - (235-16*2^2)}{2.1-2}\\\\ y(2.1,2) = -65.6 \ m/s

    (2)

    y(2.05,2) = \frac{(235-16*2.05^2) - (235-16*2^2)}{2.05-2}\\\\ y(2.05,2) = -64.8 \ m/s

    (3)

    y(2.01,2) = \frac{(235-16*2.01^2) - (235-16*2^2)}{2.01-2}\\\\ y(2.01,2) = -64.16 \ m/s

    b. y = 235 – 16t²

    The instantaneous velocity is given by;

    v = dy /dt

    dy / dt = -32t

    when t = 3 s

    v = -32(3)

    v = -96 m/s

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