a rocket sled is propelled along a verticle circular track with a radius of 100.
ID: 1986082 • Letter: A
Question
a rocket sled is propelled along a verticle circular track with a radius of 100. taking the center of the circle (100m off the ground) as the origin of your coordinate system, the equations of motion are given by r=100m and =-/2+2t2
a) evaluate the vector velocity and the vector acceleration as functions of time in polar cooridinates.
b)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 only influenced by gravity. ignoring air resistance, how far away from the bottom of the circle will the sled land
Explanation / Answer
The radius of circular track r = 100 m the equations of motion for this are ? = -(p/2) + 2t^2 or (d?/dt) = 4t or w = 4t 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 b)the distance from the bottom of the circle the sled strikes the 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 Hope that's right.
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