A rocket is moving in a planar trajectory with a velocity v = C(sub1)t^3 + C(sub
ID: 1276019 • Letter: A
Question
A rocket is moving in a planar trajectory with a velocity v = C(sub1)t^3 + C(sub2)t^5 j, where C(sub1) and C(sub2) are constants with the correct units, and either C(sub1) or C(sub2) is negative (but NOT both). There is no external source of acceleration: all of the acceleration comes from the rocket's engines.
(a) Find the time, in terms of C(sub1) and C(sub2), at which the velocity and acceleration are perpendicular to each other.
(b) Interpret the result: what kind of motion is taking place here? In particular, what would happen if both C(sub1) and C(sub2) were positive?
Explanation / Answer
a=dv/dt=3C1t^2i+5C2t^4j
v=C1t^3i+C2t^5j
a)for velocity and acceleration to be perpendicular,
v.a=0
3C1^2*t^5+5C2^2t^9=0
t^5(3C1+5C2*t^4)=0
3C1+5C2*t^4=0
t=(-3C1/5C2)^1/4
b)since velcity and acceleration are perpendicular, the motion is circular at that instant in time.
If the signs were same, at no point in the motion would be circular.
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