A rocket sled accelerates from rest for a distance of 645 m at 16.0 m/s2. A parachute is then used to slow it down to a stop. If the parachu

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A rocket sled accelerates from rest for a distance of 645 m at 16.0 m/s2. A parachute is then used to slow it down to a stop. If the parachute gives the sled an acceleration of -18.2 m/s2 and there is 500.0 m of sled track remaining after the shoot opens, will the sled stop before running off the track? Show why or why not?

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Sigridomena 4 years 2021-09-04T06:07:51+00:00 1 Answers 108 views 0

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  1. niczorrrr
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    2021-09-04T06:09:07+00:00
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    Answer:

    the stopping distance is greater than the free length of the track, the vehicle leaves the track before it can brake

    Explanation:

    This problem can be solved using the kinematics relations, let’s start by finding the final velocity of the acceleration period

              v² = v₀² + 2 a₁ x

    indicate that the initial velocity is zero

              v² = 2 a₁ x

    let’s calculate

              v = \sqrt {2 \ 15.0 \ 645}

              v = 143.666 m / s

    now for the second interval let’s find the distance it takes to stop

              v₂² = v² – 2 a₂ x₂

    in this part the final velocity is zero (v₂ = 0)

             0 = v² – 2 a₂ x₂

             x₂ = v² / 2a₂

    let’s calculate

             x₂ = \frac{ 143.666^2 }{2 \ 18.2}

             x₂ = 573 m

    as the stopping distance is greater than the free length of the track, the vehicle leaves the track before it can brake

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