A projectile is given an initial velocity of (i + 2j) m/s, where, i is along the ground and j is along the vertical. If g = 10 m/s², then the equation of its trajectory is

A projectile is given an initial velocity of (i + 2j) m/s,… — JEE Main 2013 Physics PYQ

JEE Main 2013

A projectile is given an initial velocity of

(\hat{i} + 2\hat{j})

m/s, where,

\hat{i}

is along the ground and

\hat{j}

is along the vertical. If

g = 10

m/s², then the equation of its trajectory is

A.
$y = x - 5x^2$
B.
$y = 2x - 5x^2$
C.
$4y = 2x - 5x^2$
D.
$4y = 2x - 25x^2$

Show answer and solution

Correct option: B

Solution

The initial velocity components are u_x = 1 m/s and u_y = 2 m/s. The trajectory equation is y = (u_y/u_x)x − (g/(2u_x²))x². Substituting: y = (2/1)x − (10/(2×1))x² = 2x − 5x².

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