Consider a projectile that is thrown upward at an angle between 10 and 80 degrees from the horizontal, when are the acceleration and velocity vectors perpendicular to each other?
(Only consider the motion during free fall.)
a) nowhere
b)at the highest point
c)the launch point
d)the landing point
- i am thinking it be at the highest point ? but I want to make sure
To determine when the acceleration and velocity vectors are perpendicular to each other during the projectile's motion, we need to analyze the components of the acceleration and velocity vectors separately.
The acceleration vector of a projectile during free fall is always downward, due to the force of gravity. This means that the vertical component of the projectile's acceleration is always directed downward, while the horizontal component remains zero throughout the entire motion.
On the other hand, the velocity vector of the projectile has both vertical and horizontal components. Initially, when the projectile is launched, the velocity vector is not perpendicular to the acceleration vector, as it has both horizontal and vertical components. As the projectile ascends, the vertical component of velocity decreases due to the opposing acceleration from gravity.
At the highest point of the projectile's trajectory, the vertical velocity component becomes zero. However, the horizontal velocity component still exists and is never affected by the acceleration due to gravity. Therefore, at the highest point, the vertical component of the velocity vector is zero, and only the horizontal component remains, making the acceleration and velocity vectors perpendicular to each other.
So, the correct answer would be:
b) at the highest point