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Black_prince [1.1K]
4 years ago
8

Suppose an object moves in an elliptical orbit parametrized by x = 4 cos t and y = 6 sin t, where t ≥ 0. use (4) and (5) in sect

ion 6.8 in order to find a formula for the velocity v(t) of the object at a given time t. then determine the value of the velocity at the indicated times:
Physics
1 answer:
omeli [17]4 years ago
3 0

As we know that position is given as

x = 4 cost , y = 6 sint

now in order to find the velocity

\frac{dx}{dt} = v_x

so here we will have

v_x = \frac{d}{dt} 4cost = -4sint

similarly in y direction

v_y = \frac{dy}{dt}

v_y = \frac{d}{dt}(6sint) = 6 cost

now the net velocity is given as

v = \sqrt{v_x^2 + v_y^2}

v = \sqrt{(-4sint)^2+(6cost)^2}

v = \sqrt{16sin^2t + 36 cos^2t}

<em>so above is the velocity as a function of time</em>

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