Object A has a position as a function of time given by _A(t) = (3.00 m/s) tî + (1.00 m/s2) t2ĵ. Object B has a position as a function of time given by
_B(t) = (4.00 m/s) tî + (-1.00 m/s²) t²ĵ. All quantities are SI units. What is the distance between object A and object B at time t = 3.00 s?

Question

Object A has a position as a function of time given by

_A(t) = (3.00 m/s) tî + (1.00 m/s2) t2ĵ. Object B has a position as a function of time given by Object A has a position as a function of time given by A(t) = (3.00 m/s) tî + (1.00 m/s2) t2ĵ. Object B has a position as a function of time given by B(t) = (4.00 m/s) tî + (-1.00 m/s2) t2ĵ. All quantities are SI units. What is the distance between object A and object B at time t = 3.00 s? A) 34.6 m B) 15.0 m C) 18.3 m D) 3.46 m E) 29.8 m

_B(t) = (4.00 m/s) tî + (-1.00 m/s²) t²ĵ. All quantities are SI units. What is the distance between object A and object B at time t = 3.00 s?

Quizplus · Accepted Answer

The distance between Object A and Object B is given by the magnitude of the vector difference of their positions:
|RA-RB| = sqrt[(xA-xB)^2 + (yA-yB)^2]

Substituting in the given expressions for the positions at t=3s:

|RA-RB| = sqrt[((3.00 m/s)(3.00 s) - (4.00 m/s)(3.00 s))^2 + ((1.00 m/s^2)(3.00 s)^2 - (-1.00 m/s^2)(3.00 s)^2)^2]
        
|RA-RB| = 18.3 m

Therefore, the answer is choice C.

Object a Has a Position as a Function of Time