(Test Your Understanding of Section 3.2)
The question wants me to choose the correct acceleration vector, from the given 9 options where 9th option is zero acceleration.
Ok, first I thought option 9 (zero acceleration) is the correct answer here. The sled’s speed decreases as it goes up the hill, because in this case there is a parallel component of gravitational acceleration, i.e $g\sin\theta$, that is acting opposite to the velocity of the sled. (There is a perpendicular component $g\cos\theta$ too, but that is only changing the direction of the velocity).
Likewise, sled’s velocity increases as it goes down the hill because ‘$g\sin\theta$’ in this case is acting along the direction of the sled’s instantaneous velocity. But when the sled is at the crest of the curved trajectory, the sled’s velocity instantaneously becomes constant because parallel component of acceleration, i.e $g\sin\theta$ is zero. And I thought that the perpendicular component of $g$, or $g\cos\theta$ is getting cancelled out by the normal force acting on the sled. That’s why I thought option 9 was correct, i.e zero acceleration when the sled is at the crest of the hill.
But the answer at the end of the chapter says that option 7 is correct. How can option 7 be correct, because the sled isn’t moving vertically upwards, or vertically downwards when it is at the crest of the hill. Then how can we say that option 7 is correct?
Also, in the question above that ($conceptual$ $example$ $3.4$), how is the direction of acceleration at $Point$ $E$ vertically upwards?