To model a spacecraft, a toy rocket engine is securely fastened to a large puck, which can glide with negligible friction over a horizontal

To model a spacecraft, a toy rocket engine is securely fastened to a large puck, which can glide with negligible friction over a horizontal surface, taken as the xy plane. The 8.00 kg puck has a velocity of 10.0 i hat m/s at one instant. Eight seconds later, its velocity is to be (10.0 i hat 12.0 j) m/s. (a) Assuming the rocket engine exerts a constant total horizontal force, find the components of the force. ( i hat j ) N (b) Find its magnitude. N

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  1. Explanation:

    Given that,

    Mass of a puck, m = 8 kg

    Initial velocity, u = 10i m/s

    Final velocity, v = (10i+12j) m/s

    Time, t = 8 s

    (a) Force acting on an object is given by the product of mass and acceleration.

    F = ma

    a is acceleration

    [tex]F=\dfrac{m(v-u)}{t}\\\\F=\dfrac{8\times (10i+12j-10i)}{8}\\\\F=12j\ \text{N}[/tex]

    (b) The magnitude of force is given by :

    [tex]F=\sqrt{12^2+0^2} \\\\F=12\ N[/tex]

    Hence, the component of force is 12j N and its magnitude is 12 N.

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