A particle is on a circular path with a constant radius of 200 m as shown in the

Question

A particle is on a circular path with a constant radius of 200 m as shown in the attached diagram. At the instant shown in the diagram, the speed is 5 km/s and it is accelerating at 2 km/s2 in the direction of motion. Determine at the instant of time shown:

a.) The velocity vector in Tangent-Normal (et and en) components
b.) The acceleration vector in Tangent-Normal (et and en) components
c.) Express the unit vectors et and en in rectangular unit vectors, i and j.

A particle is on a circular path with a constant radius of 200 m as shown in the attached diagram. At the instant shown in the diagram, the speed is 5 km/s and it is accelerating at 2 km/s2 in the direction of motion. Determine at the instant of time shown: The velocity vector in Tangent-Normal (et and en) components The acceleration vector in Tangent-Normal (et and en) components Express the unit vectors et and en in rectangular unit vectors, i and j.

Explanation / Answer

It is not mentioned clearly whether the particle is moving tangential to circle.,

if assumed tangential ., then

et =5 km/sec,.ev = 0 km/sec

an = v^2/r = (5000)^2/200 =125 Km /sec^2

at = 2Km/sec ^2

now making them into unit vectors perpendicular to x,y

ax = at cos 60 + an sin 60 = 109.253 m/s^2 i

ay = at sin 60 - an cos 60 =-60.76 m/s^2 j

unit vectors = 0.874 i + 0.486 j

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