Question

A projectile is given an initial velocity of $(\hat{i} + \hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical direction. The equation of its trajectory is $(g = 10 \, \text{m/s}^2)$.

• A. $y^2 = 2x$
• B. $y^2 - 1 = 5x$
• C. $y = x - 5x^2$
• D. $y = x^2$
• E. $y = x^2 - 2$

Hint:

For projectile motion, always use the standard trajectory equation and substitute known values carefully.

Answer 1

The Correct Option is C

Step 1: The general equation of projectile motion is given by: \[ y = x \tan{\theta} - \frac{g x^2}{2 u^2 \cos^2{\theta}} \] Step 2: Given initial velocity components: \[ u_x = 1, \quad u_y = 1 \] Step 3: Using $\theta = 45^\circ$, $\tan{\theta} = 1$, and substituting values: \[ y = x - \frac{10x^2}{2(1)^2} \] \[ y = x - 5x^2 \] Step 4: Therefore, the correct answer is (C).