A projectile is fired from the surface of the earth with a velocity of 5 m s^$$-$$1 and angle $$\theta $$ with the horizontal. Another projectile fired from another planet with a velocity of 3 m s^$$-$$1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s^$$-$$2) is
(Given g = 9.8 m s^$$-$$2)

Vectors $$\overrightarrow A ,\overrightarrow B $$ and $$\overrightarrow C $$ are such that $$\overrightarrow A .\overrightarrow B = 0$$ and $$\overrightarrow A .\overrightarrow C = 0$$. Then the vector parallel to $$\overrightarrow A $$ is

The velocity of a projectile at the initial point A is $$\left( {2\widehat i + 3\widehat j} \right)$$ m/s. It's velocity (in m/s) at point B is

A particle has initial velocity $$\left( {2\overrightarrow i + 3\overrightarrow j } \right)$$ and acceleration $$\left( {0.3\overrightarrow i + 0.2\overrightarrow j } \right)$$. The magnitude of velocity after 10 seconds will be