Projectile from a Non-Inertial or Moving Frame

The question involves projectile motion observed from or launched within a non-inertial reference frame (e.g., an accelerating train) or requires optimizing launch from a moving platform.

jee-main 2013 Q2 View
The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R _ { 0 } = 40 \mathrm {~m}$. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $\mathrm { v } = 20 \mathrm {~m} / \mathrm { s }$ on a horizontal surface? $\left( \mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 } \right)$
(1) $30 ^ { \circ }$
(2) $60 ^ { \circ }$
(3) $75 ^ { \circ }$
(4) $45 ^ { \circ }$
jee-main 2021 Q5 View
A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a:
(1) straight line vertically down the plane
(2) parabola in a direction opposite to the motion of plane
(3) parabola in the direction of motion of plane
(4) hyperbola
jee-main 2025 Q50 View
The maximum speed of a boat in still water is $27\,\mathrm{km/h}$. Now this boat is moving downstream in a river flowing at $9\,\mathrm{km/h}$. A man in the boat throws a ball vertically upwards with speed of $10\,\mathrm{m/s}$. Range of the ball as observed by an observer at rest on the river bank, is \_\_\_\_ cm. (Take $g = 10\,\mathrm{m/s^2}$)