Question

The path of one projectile as seen by an observer on another projectile is a/an:

• A. straight line
• B. parabola
• C. ellipse
• D. circle

Answer 1

Answer: (A)

We know that

$x=(ucos\theta )t$ and $y=(usin\theta )t-\frac{1}{2}g{t}^2$

Let $x_2-x_1=(u_{1}cos{\theta }_1-u_{2}cos{\theta }_2)t=X$

$y_2-y_1=(u_{1}sin{\theta }_1)t-\frac{1}{2}g{t}^2$

$-(u_{2}sin{\theta }_2)t+\frac{1}{2}g{t}^2$

$=(u_{1}sin{\theta }_1-u_{2}sin{\theta }_2)t=Y$

$\frac{Y}{X}=\frac{(u_{1}sin{\theta }_1-u_{2}sin{\theta }_2)t}{(u_{1}cos{\theta }_1-u_{2}cos{\theta }_2)t}$

$=\frac{u_{1}sin{\theta }_1-u_{2}sin{\theta }_2}{u_{1}cos{\theta }_1-u_{2}cos{\theta }_2}$

= constant, m (say)

Y= m X

It is the equation of a straight line passing through the origin.