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30 December, 08:15

0 A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is _ five feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile?

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  1. 30 December, 08:37
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    a) nearest jump is JL = 1380 inches = 115ft

    b) number of jumps in 1 mile N = 46 jumps

    Step-by-step explanation:

    Given that the jump length is proportional to the body length.

    If 2 inch grasshopper can jump 40 inches.

    JL = k (BL)

    k = JL/BL

    where JL = jump length = 40 inches

    BL = Body length = 2 inches.

    k = 40/2 = 20

    The constant of proportionality is 20.

    For the athlete:

    BL = 5ft 9 inches = 5 (12) + 9 = 69 inches.

    The jump length of the athlete is:

    JL = k (BL) = 20 (69)

    JL = 1380 inches. = 115ft

    The number of jumps in 1 mile is

    1 mile = 63360 inches

    N = 63360/1380

    N = 45.9 = 46

    N = 46

    Therefore, 46 jumps would be needed.
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