A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.20-kg puck has a velocity of 1.60î m/s at one instant. Eight seconds later, its velocity is (6.00î + 4.0ĵ) m/s. (a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force.

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ajdonis ajdonis · Answer 1 · 2019-10-15T02:18:12+02:00

Answer:

[tex]F_{x}=2.31N [/tex] to the right.

[tex]F_{y}=2.1N [/tex] to in the upwards direction.

Explanation:

In order to solve this problem, we must first start by drawing a diagram of the situation. (See attached diagram).

So, remember that a force is determined by multiplying the mass of the parcticle by its acceleration:

F=ma

so in order to find the components of the force, we need to start by finding its acceleration.

Acceleration is found by using the following formula:

[tex]a=\frac{V_{f}-V{0}}{t}[/tex]

so we can subtract the two vectors, like this:

[tex]a=\frac{(6.00i+4.0j)m/s-1.60i m/s}{8s}[/tex]

which yields:

[tex]a=\frac{(4.4i+4.0j)m/s}{8s}[/tex]

or:

[tex]a=(0.55i + 0.5j) m/s^{2}[/tex]

so now I can find the components of the force:

[tex]F=(4.2kg)(0.55i + 0.5j) m/s^{2}[/tex]

which yields:

F=(2.31i+2.1j)N

so the components of the force are:

[tex]F_{x}=2.31N [/tex] to the right.

[tex]F_{y}=2.1N [/tex] to in the upwards direction.