Two points in the x y plane have Cartesian coordinates (2.00,-5.00) m and (-8.00

Question

Two points in the x y plane have Cartesian coordinates (2.00,-5.00) m and (-8.00, 8.00) m. a) Determine the distance between these points. b) Determine their polar coordinates, r, 5. A billiard ball undergoes two displacements. The first has a magnitude of 150 cm and makes an angle of an angle of 35.00 to the positive x-axis. Find the magnitude and direction of the second displacement. 6. It is possible to shoot an arrow at a speed as high as 125 m/s (a) If friction is neglected, how high would an arrow launched at this speed rise if shot straight up? (b) How long would the arrow be in the air? In a linear accelerator, an electron is accelerated to 1 .00% of the speed of light in 40.0 m before it coasts 60.0 m to target. (a) What is the electron's acceleration during the first 40.0 m? (b) How long does the total flight take? 7.

Explanation / Answer

4. (A) distance = sqrt[ (x2 - x1)^2 + (y2 - y1)^2 ]

= 16.4 m

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

and theta = tan^-1(y/x)

for (2, - 5)

r = sqrt(2^2 + (-5)^2) = 5.4 m

theta = 360 - tan^-1(5/2) = 292 deg

Ans: 5.4 m , 292 deg

for (-8 , 8)

r = 11.3 m

theta = 180 - tan^-1(8/8) = 135 deg

Ans: 11.3 m , 135 deg

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