Question

A body is projected horizontally from a point above the ground. The motion of the body is defined by $x=2t$ and $y=2t^2$, where x and y are horizontal and vertical displacement respectively from initial position at time $t$. Which of the following is/are true ?

• A. The trajectory of the body is a parabola.
• B. The trajectory of the body is a straight line.
• C. The velocity vector at a point is $2\hat{i}+4t\hat{j}$.
• D. The acceleration vector at time t is $4\hat{j}$.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The trajectory of the body is a parabola.
C The velocity vector at a point is $2\hat{i}+4t\hat{j}$.
D The acceleration vector at time t is $4\hat{j}$.

Given $x=2t$, $y=2t^2$
Eliminating $t$, we get $y=x^2/2$
So it is a parabola.

$v_x=\frac{dx}{dt}=2$
$v_y=\frac{dy}{dt}=4t$

So velocity at any time $t$ is given by
$v=2\hat{i}+4t\hat{j}$

Now similarly,
$a_x=\frac{d{v}_x}{dt}=0$
$a_y=\frac{d{v}_y}{dt}=4$

So acceleration vector is $a=4\hat{j}$