Billy Bob caved, and bought a Bugatti because, he could not afford a Hennessey V

Question

Billy Bob caved, and bought a Bugatti because, he could not afford a Hennessey Venom GT. In his 1^st Saturday test drive, Billy Bob drove 30 km due east, out in the sticks on Hwy-6, on his way to catch the Houston Rodeo. He got hungry, and turned due north and drove "wide-open" for another 40 km to get some Texas-style BBQ. What is the resultant displacement distance, and direction, of Billy Bob's Bugatti during his jog to get some BBQ? Choose the closest answer from those provided below (Don't work too hard). a) 50 km, 53.13 degree NE: b) 75 km, 30 degree NE: c) 39 km, 24 degree NE: or d) 48 km, 36.9 degree NE.

Explanation / Answer

initial displacement, ri = 30 i <--------- i = unit vector due East

final displacement, rf = 40 j <---------- j = unit vector due North

So, total displacement , rtot = ri + rj

= 30 i + 40 j

So, magnitude of displacement = sqrt(30^2 + 40^2) = 50 km <------ answer

direction of displacment = atan(40/30) = 53.13 deg NE <----- answer

So, answer is option (a) 50 km, 53.13 NE

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