When a ball is thrown with a velocity of $50 \ m s^{-1}$ at an angle $30^{\circ}$ with the horizontal,it remains in the air for how many seconds? (Take $g = 10 \ m s^{-2}$)

$A$ particle is projected with velocity $u$ at an angle $\alpha$ with the horizontal,and another particle is projected with the same velocity $u$ at an angle $\alpha$ with the vertical. What is the ratio of their times of flight?

$A$ player kicks a ball at a speed of $20 \ ms^{-1}$ so that its horizontal range is maximum. Another player $24 \ m$ away in the direction of the kick,starts running in the same direction at the same instant the ball is kicked. If he has to catch the ball just before it reaches the ground,he should run with a velocity equal to: (Take $g = 10 \ ms^{-2}$)

$A$ projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal direction with a velocity of $150\, ms^{-1}$. Then the time after which its inclination with the horizontal is $45^{\circ}$ is

$A$ bomb is released from a horizontal flying aeroplane. The trajectory of the bomb is

$A$ projectile is thrown at an angle $\theta$ with the horizontal and its range is $R_1$. It is then thrown at an angle $\theta$ with the vertical and the range is $R_2$. Then: