A river flows due south with a speed of 2.0 m/s. You steer a motorboat across the river; your velocity relative to the water is
4.2 m/s due east. The river is 500 m wide. (a) What is your velocity (magnitude and direction) relative to the earth? (b) How much time is required to cross the river? (c) How far south of your starting point will you reach the opposite bank?
1 answer:
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Answer:
I₁ = (7.78 i ^ - 6.71 j ^) 10⁻³ J s , I₂ = (-12.5 i ^ -14.6 j ^) 10⁻³ J s , I₃ = (19.1i ^ + 18.6 j ^) 10⁻³ J s and I₄ = (-9.14i ^ + 7.24 j ^) 10⁻³ J s
Explanation:
The impulse is equal to the variation of the moment, to apply this relationship to our case, we will assume that initially the mouse was at rest
I = Δp = m -m v₀
I = m ( -v₀)
Bold indicates vector quantities, let's calculate the momentum of each mouse in for the x and y axes
We recommend bringing all units to the SI system
Mouse 1.
It has a mass of 22.3 g = 22.3 10⁻³ kg, a final velocity of (v = 0.349 i ^ - 0.301 j ^) m / s with an initial velocity of zero
Iₓ = m ( - v₀ₓ)
Iₓ = 22.3 10⁻³ (0.349 -0)
Iₓ = 7.78 10⁻³ J s
= m (
-
)
= 22.3 10⁻³ (-0.301)
= -6.71 10⁻³ J s
I₁ = (7.78 i ^ - 6.71 j ^) 10⁻³ J s
Mouse 2
Mass 17.9 g = 17.9 10⁻³ kg
Speed (-0.699 i ^ - 0.815 j ^) m / s
Iₓ = m ( - v₀ₓ)
Iₓ = 17.9 10⁻³ (-0.699 -0)
Iₓ = -12.5 10⁻³ J s
= 17.9 10⁻³ (-0.815 - 0)
= -14.6 10⁻³ J s
I₂ = (-12.5 i ^ -14.6 j ^) 10⁻³ J s
Mouse 3
Mass 19.1 g = 19.1 10⁻³ kg
Speed (0.745i ^ + 0.975 j ^) m / s
Iₓ = 19.1 10⁻³ (0.745 -0)
Iₓ = 14.2 10⁻³ J s
= 19.1 10⁻³(0.975 -0)
= 18.6 10⁻³ J s
I₃ = (19.1i ^ + 18.6 j ^) 10⁻³ J s
Mouse 4
Mass 10.1 g = 10.1 10⁻³ kg
Speed (-0.905i ^ + 0.717j ^) m / s
Iₓ = 10.1 10⁻³ (-0.905 -0)
Iₓ = -9.14 10⁻³ J s
= 10.1 10⁻³ (0.717 -0)
= 7.24 10⁻³ J s
I₄ = (-9.14i ^ + 7.24 j ^) 10⁻³ J s