Question

For a projectile, which of the following quantities are constant during the flight: $x,y,r,v_x,v_y,v,a_x,a_y$? Which of these quantities are zero throughout the flight?

Short answer

$a_x$remains zero throughout the flight.

Step-by-step solution

Step.1

Projectile motion is study of motion of an object thrown near the Earth surface. In this motion the object moves in two dimensions by following a curved path and the only acceleration is due to gravity.

When the object was thrown upwards making some angle with the horizontal, the magnitude of the position vector is expressed as,

$r=\sqrt{x^2+y^2}$

Here, $x$and $y$are horizontal and vertical displacements respectively.

The magnitude of its velocity is,

$v=\sqrt{v_x^2+v_y^2}$

Here, $v_x$and $v_y$are horizontal and vertical components of velocity.

Step.2

The vertical component of velocity decreases while going up and increases while coming down due to downward acceleration $\left(a_y=g\right)$. However, the horizontal component of velocity $\left(v_x\right)$ remains constant as there is no horizontal acceleration $\left(a_x=0\right)$. But due to initial horizontal velocity, the object undergoes horizontal displacement $\left(x\right)$.

Since,$v_y$ is not constant$v$is also not constant and$r$also changes. The vertical component of acceleration is equal to acceleration due to gravity which is a constant.

Therefore, the quantities $a_x,a_y$ and $v_x$remain constant during the flight.

Step.3.

From the above discussion, the horizontal component of acceleration$a_x$is always zero throughout the flight.

Therefore, only $a_x$remains zero throughout the flight.