Answer to Question #313069 in Physics for dsasa

Question

Phineas is pushing a 11.13-kg box of tools with a force of 47 N directed at an angle of 83° downward from the horizontal. How fast is the cart going after the acceleration from rest if their backyard is 77 cm away from the garage?

Answer 1

The horizontal component of applied force

$$F_x=F\cos\theta\\ =47\:\rm N*cos83^\circ=5.73\: N$$

The acceleration of the box

$$a=\frac{F_x}{m}=\frac{5.73\:\rm N}{11.13\:\rm kg}=0.515\:\rm m/s^2$$

The final velocity

$$v=\sqrt{2ad}\\ =\sqrt{2*0.515\:\rm m/s^2*0.77\: m}=0.89\:\rm m/s$$