A point has rectangular coordinates x = 4.0 and y = 7.0. Find the components r a

Question

A point has rectangular coordinates x = 4.0 and y = 7.0. Find the components r and theta of the point. r - component theta-component, relative to positive x-axis W thin the jet stream, a plane flies 156 m/s at 75.0 degree South of West The jet stream itself is moving 115 North Find the velocity of the jet relative to the ground. magnitude direction (relative to +x-axis) A car drives straight off the edge of a cliff that is 84.0 m high. The police at the scene of the accident the point of impact is 125 m from the base of the cliff. How fast was the car traveling when it cliff?

Explanation / Answer

8. coordinates : (x , y ) = (4, 7 )

r = sqrt(x^2 + y^2) = 8.062

ans(a)

9. @ = tan^-1(y/x) = tan^-1( 7/4) = 60.26 deg

Ans(c)

10. velocity of plane vp = 156(-cos75i - sin75j) = -40.38i - 150.68j m/s

velocity of stream Vs = 115 j m/s

velocity of plane wrt ground v = vp + vs = - 40.38i - 35.68 j m/s

magnitude = sqrt(40.38^2 + 35.68^2) = 53.88 m/s

11. angle to the +ve x axis in counterclockwise direction = 180 + tan^-1(35.68 / 40.38)

          = 221.46 deg

Or 360 - 221.46 = -138.5 deg

Ans (b)

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