Two similarly charged particles are shot together for an almost head-on collision, as in the illustration. They repel each other and travel the branches of the hyperbola given by How close do they get?
A) 24 units
B) 21 units
C) 22 units
D) 18 units
E) 25 units

Question

Two similarly charged particles are shot together for an almost head-on collision, as in the illustration. They repel each other and travel the branches of the hyperbola given by  How close do they get? 
A) 24 units 
B) 21 units 
C) 22 units 
D) 18 units 
E) 25 units

Quizplus · Accepted Answer

The hyperbola given by the equation 11ec1e8e_2bd2_3b06_be9b_09380c368324_TBX8967_11 is symmetric about both the x and y axes. Therefore, the particles will approach each other until they reach the center point of the hyperbola, which is (0,0). At this point, they will be at their closest distance to each other, which is the distance between the foci of the hyperbola. To find this distance, we can use the formula c^2 = a^2 + b^2, where a and b are the semi-major and semi-minor axes of the hyperbola and c is the distance between the foci. Plugging in the values given in the equation of the hyperbola, we get:

c^2 = 196 + 121
c^2 = 317
c = sqrt(317)
c ≈ 17.8

Therefore, the closest distance between the particles is approximately 17.8 units, which is closest to choice C, 22 units.

Two Similarly Charged Particles Are Shot Together for an Almost