On a spacecraft two engines fire for a time of 565 s. Onegives the craft an acce

Question

On a spacecraft two engines fire for a time of 565 s. Onegives the craft an acceleration in the x direction ofax = 5.10 m/s2, while the otherproduces an acceleration in the y direction ofay = 7.30 m/s2. At the end of thefiring period, the craft has velocity components ofvx = 3865 m/s and vy = 4266m/s. Find the magnitude and direction of the initial velocity.Express the direction as an angle with respect to the +xaxis.
I'm totally stuck on this, please help!! Thanks!
On a spacecraft two engines fire for a time of 565 s. Onegives the craft an acceleration in the x direction ofax = 5.10 m/s2, while the otherproduces an acceleration in the y direction ofay = 7.30 m/s2. At the end of thefiring period, the craft has velocity components ofvx = 3865 m/s and vy = 4266m/s. Find the magnitude and direction of the initial velocity.Express the direction as an angle with respect to the +xaxis.
I'm totally stuck on this, please help!! Thanks!

Explanation / Answer

   Let unit vectors along X and Y axis be i^and j^, respectively.    a   =   ax* i^   +   ay *j^   =   5.10 *i^   +   7.30 *j^     m/s2    And         v   =   vx* i^   +   vy *j^   =   3865 *i^   +   4266 *j^   m/s    According to first equation of motion    v   =   u + a*t,   u   =   ux* i^   +   uy * j^    u denotes initial velocity.    3865 *i^   +   4266 *j^   =   u   +   (5.10* i^   +   7.30 * j^) * 565    u   =   (3865- 5.10 * 565) * i^   +   (4266 -7.30 * 656) * j^   =   983.50 *i^   +   141.50 *j^      m/s    initialvelocity      u   =   (ux2   +   uy2)   =   (983.502   +   141.502)   =   993.63   m/s    Angle with Xaxis      tan   =   uy /ux       =   tan-1(141.5 /983.5)   =   8.190       =   tan-1(141.5 /983.5)   =   8.190     

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