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

`F_(x)=2.31N` to the right.

`F_(y)=2.1N` to in the upwards direction.

Step-by-step 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=((6.00i+4.0j)m/s-1.60i m/s)/(8s)`

which yields:

`a=((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.