3) A rocket sled is propelled along a vertical circular track with radius 100 m.

Question

3) A rocket sled is propelled along a vertical circular track with radius 100 m. Taking the center of the circle (100 m off the ground) as the origin of your coordinate system, the equations of motion are given by r-100, =-/2 + 2t2 Evaluate the vector velocity and the vector acceleration as functions of time in polar coordinates. When the sled reaches = /4, two failures occur at the same time. The rocket sled runs out of fuel and the track breaks. The sled therefore goes flying off on a trajectory influenced only by gravity. (Ignore air resistance.) How far away fromm the bottom of the circle will the sled strike the ground? a. b.

Explanation / Answer

3) Given that

Radius of circular track r = 100 m

The equations of motion are

= -(/2) + 2t^2

or (d/dt) = 4t

or w = 4t

Part-A

the vector velocity is

v = r * w = 100 * 4t = 400t

the vector acceleration is

a = (v^2/r) = ((400t)^2/100) = 1600 * t^2

Part-B

the distance from the bottom of the circle the sled strikethe ground is

v^2 - u^2 = 2gS)

or S = (v^2 - u^2/2g)

or S = ((400t)^2 - (0)^2/2 * 9.8) = 8163.2 * t^2

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