Useful background for this problem can be found in Multiple-Concept Example 2. O

Question

Useful background for this problem can be found in Multiple-Concept Example 2. On a spacecraft two engines fire for a time of 657 s. One gives the craft an acceleration in the x direction of a_x = 9.86 m/s^2, while the other produces an acceleration in the y direction of a_y = 7.26 m/s^2. At the end of the firing period, the craft has velocity components of v_x = 7900 m/s and v_y = 6080 m/s. Find (a) the magnitude and (b) the direction of the initial velocity. Express the direction as an angle with respect to the +x axis. (a) Number Units (b) Number Units

Explanation / Answer

v = v0 + a t

Along x axis,

v_x = v0x + ax t

7900 = v0x + (9.86)(657)

v0x = 1422 m/s

v_y = v0y + ay t

6080 = v0y + (7.26)(657)

v0y = 1310.2 m/s

(A) magnitude = sqrt(v0x^2 + v0y^2) = 1933.56 m/s

(B) Direction = tan-1(v0y / v0x) = 42.6 deg

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