Question

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.

Answer 1

Answer:

$F_{x}=2.31N$ to the right.

$F_{y}=2.1N$ 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:

$a=\frac{V_{f}-V{0}}{t}$

so we can subtract the two vectors, like this:

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

which yields:

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

or:

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

so now I can find the components of the force:

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

which yields:

F=(2.31i+2.1j)N

so the components of the force are:

$F_{x}=2.31N$ to the right.

$F_{y}=2.1N$ to in the upwards direction.