1. A particle\'s position on the x-axis is given by the function x=(t^2 - 6.00*t

Question

1. A particle's position on the x-axis is given by the function x=(t^2 - 6.00*t+ 4.00)   m, where t is in s. Where is the particle when vx = 5.00 m/s ?
2. A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30 m/s^2 for 32 s , then runs out of fuel. Ignore any air resistance effects.
a) What is the rocket's maximum altitude?
b) How long is the rocket in the air before hitting the ground?
3. Find x- and y-components of the following vectors.
a) r? = (660m, 36 degrees below positive x axis)
b) v? = (710 m/s,26 degrees above positive x axis)
c) a? = (3.8 m/s^2 ,negative y direction)

Explanation / Answer

1.

The particle speed is the derivative
v = dx/dt = 2t - 6.00
so
t = (v + 6.00)/2

When v = 5.00 m/s
t = (5.00 + 6.00)/2 = 5.5 s

Then the particle position is
x = 5.00

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