Easy Physics Question Please Help?

Question

an object is thrown upward at an angle x above the ground, eventually returning to earth.
a) is there any place along the trajectory where the velocity and acceleration are perpendicular?
b)Is there any place where the velocity and acceleration are parallel? If so, where? In each case, explain.
**I think that i need to find the acc. and velocity. but how do i compares in term of perpendicular and parallel?

Answer 1

In this question, acceleration will always be directly at Earth. So acc. points straight down the whole time. Perpendicular would be when velocity points directly to the right or to the left, and this will occur when the object reaches is maximum height, and the velocity moves form upward pointing to downward pointing.

In the case of parallel, it will only occur if x=90 degrees, and velocity will always be parallel in that case.

Answer 2

a) Yes, the place is where the object has reached its max. height.
The velocity here is in a direction parallel to the ground, & its acceleration is that caused by gravity, since gtavity is the only force acting on it at this point of time, 'coz the acceleration with which it was thrown will continuously decrease during its motion until it becomes 0 at the position in which the object attains maximum height, & that is why the object begins to fall downwards from this place onwards ( It does not fall vertically downward becuse of the inertia it gained previously because of its motion).

b) There would be no place where v & a would be parallel, unless the angle x is non-zero & non 90 degree. If x=0 or 90 degrees & acceleration due to gravity acting on it = 0, then v & a will be parallel to each other. Further, if no frictional force is acting on the object due to the medium in which the object is thrown ( air on earth, normally), then the object will continue its motion at uniform VELOCITY, unless some force opposes its motion.