Atoy rocket.. PHYSICS HELP

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 3.00-kg puck has a velocity of 1.40î m/s at one instant. Eight seconds later, its velocity is (6.00î + 8.0ĵ) m/s

(a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force.

(b) Find its magnitude.

Answer 1

A constant horizontal force means a constant horizontal acceleration. Looking at a bird's eye view:

In the i-direction, the object accelerated from 1.4 to 6 m/s in 8 s so the acceleration is (6 - 1.4)/8 = 0.575 m/s²

In the j-direction, the object accelerated from 0 m/s to 8 m/s in 8 seconds so the acceleration is (8 - 0)/8 = 1 m/s²

F = ma so:

F_i = (3)(0.575) = 1.73 N

and F_j = (3)(1) = 3.00 N

The magnitude of the force is calculated from the Pythagorean Theorem. F = √(F_i² + F_j²) = 3.46 N