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Sagot :
Answer:
x₁ = 3.481 m
Explanation:
In this exercise the acceleration of the dog and the sled are given, for which we can use the kinematic relations.
Let's start by fixing a reference system located on the sled and suppose that it moves to the right, the sled acceleration a₁ = 0.2 m / s, the dog is on the other side of the rope, so if the acceleration is a₂ = -0.5 m / s2, the negative sign indicates that it is moving to the left.
The initial position of the sled is x₁₀ = 0 and the initial position of the dog is x₂₀ = 12.2 m, let's write the expressions for the position
x₁ = x₁₀ + v₁₀ t + ½ a₁ t²
x₂ = x₂₀ + v₂₀ t + ½ a₂ t²
in this case the two bodies start from rest so their initial velocities are zero
we substitute the values
x₁ = 0 + 0 + ½ (0.2) t²
x₂ = 12.2 + 0 + ½ (-0.5) t²
at the point where the two meet, the position is the same
x₁ = x₂
½ 0.2 t² = 12.2 - ½ 0.5 t²
(0.1 + 0.25) t² = 12.2
t = [tex]\sqrt{ \frac{12.2}{0.35} }[/tex]
t = 5.9 s
we look for the position of the sled (subscript 1)
x₁ = ½ 0.2 5.9²
x₁ = 3.481 m
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