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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moya1316 moya1316 · Answer 1 · 2021-04-08T02:46:09+02:00

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 = [tex]\sqrt {2 \ 15.0 \ 645}[/tex]

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 = [tex]\frac{ 143.666^2 }{2 \ 18.2}[/tex]

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