Respuesta :
Since the rope is 2.5m long and it is 1.5 m above the end attached to the sledge hence
sin (theta) = 1.5 / 2.5 so that theta is 36.9 degrees or rounding it off to 37degrees
You can see for yourself that this must be true as the rope is slanted with respect to the horizontal direction and so must represent the hypotenuse and the perpendicular distance from the boys hand to the horizontal axis is 1.5m. In this case take the origin of the coordinate system at the point where the rope and the sledge are attached. I think now things are pretty clear as far as the angle in concerned.
Now with respect to this origin the horizontal component of the force is give by
Fx = F cos(theta) .... in magnitude
= 40newtons * cos(37degrees)
= 31.9newtons which is about 32newtons when rounded to 2 significant figures
sin (theta) = 1.5 / 2.5 so that theta is 36.9 degrees or rounding it off to 37degrees
You can see for yourself that this must be true as the rope is slanted with respect to the horizontal direction and so must represent the hypotenuse and the perpendicular distance from the boys hand to the horizontal axis is 1.5m. In this case take the origin of the coordinate system at the point where the rope and the sledge are attached. I think now things are pretty clear as far as the angle in concerned.
Now with respect to this origin the horizontal component of the force is give by
Fx = F cos(theta) .... in magnitude
= 40newtons * cos(37degrees)
= 31.9newtons which is about 32newtons when rounded to 2 significant figures
