Question

A particle is projected at an angle of Ф with respect to the horizontal direction. Match the following for the above motion.
(a) vₓ – decreases and increases
(b) vᵧ – remains constant
(c) Acceleration – varies
(d) Position vector – remains downward

Answer 1

a) v(x) - Remains Constant
Since, acceleration in Horizontal direction is 0.
That is,
$a(x) = 0 \\ = > \frac{d \: v(x)}{dt} = 0 \\ = > v(x) = \: constant \:$

b) v(y) - decreases then increases.
Since,
Initially gravity acts opposite to its motion, so velocity decreases till it reaches it's maximum height.
so, v(y) decreases.
After ascending maximum height, Gravity acts along its motion in y - direction.
so, v(y) increases.

Therefore, v(y) first decreases then increases.


c) Acceleration - remains downward.
Since, acceleration is only provided by Gravitational force of Earth, so it remains always downwards towards the centre of earth.

d) Position vector - varies
Since,
There are two components of velocity v(x) and v(y) which changes the position of particle at each instant of time.