Physics Prelim Motion Help Please

[my_n00bNESS]

A well-coordinated in-line skater is playing with a yo-yo while accelerating on a horizontal surface. Figure 10.35 shows that when the yo-yo is at its lowest point it makes an angle of 5° with the vertical. Determine the acceleration of the in-line skater.

Untitled.jpg

the answer is 0.86 m s^−2 to the right but how do I get to it???
Thanks any help would be much appreciated

[Fizzy_Cyst]

If you think about the forces which are acting, you have weight acting downwards and the 'net' force which is causing the acceleration acting in the direction of the motion of the skater, the yo-yo will want to stay doing what it is doing due to inertia.

If you draw a vector diagram, you will have something like the following:

vidiag.jpg

So, therefore, you can just use trig to solve:

tan (theta) = o/a = ma/mg

tan (5) = ma/mg

Tan (5) = a/g [m's cancel]

a = gTan5

(assuming on Earth, where g=9.8)

a = 9.8 * Tan(5) = 0.86ms^-2 opposite to the direction of the angle subtended to the vertical.

[my_n00bNESS]

wow thanks so much. It seemed so hard but turned out so easy. Thanks a lot.