Projectile Motion

Q. A particle is projected at an angle $\theta$ to the horizontal and it attains a maximum height H. The time taken by the projectile to the highest point, of its path is

1. $\frac{\sqrt{H}}{g}$
2. $\sqrt{\frac{2H}{g}}$
3. $\sqrt{\frac{2H\sin \theta }{g}}$
4. $\frac{\sqrt{2H}}{\sin \theta }$

Q. A stone is projected horizontally from a cliff at 10 m/sec and lands on the ground at 20 m form the bases of the cliff. Find the height of the cliff. Use $g=10m/s^2$

1. 18 m
2. 20 m
3. 22 m
4. 24 m

Q. A projectile is fired from point P at an angle of 45${}^o$ horizontally as shown below. If g is the acceleration due to gravity, then the speed required to reach a point Q lying on the horizontal surface at a distance of R from point P is

1. $\sqrt{Rg/2}$
2. $\sqrt{Rg}$
3. $\sqrt{2Rg}$
4. $\sqrt{3Rg}$

Q. Two adjacent bowling machines deliver balls at 30.5 m/s simultaneously at angles of elevation ${\alpha }_1\text{and}{\alpha }_2$ for the same target at a range of 20.13 m. Calculate the time difference between the two hits

1. 5.5 sec
2. 55 sec
3. 11 sec
4. 22 sec

Q. When a jet plane flying at 300 m/s along a circle in vertical plane, it is observed that at the top of its trajectory, the apparent weight of a passenger is one half of her actual weight. Find the radius of curvature R of the flight path at this point. Use g = 10 m/s${}^2$

1. 22 km
2. 18 km
3. 30 km
4. 16 km