Maximum Height

Q. The maximum height of a projectile for two complementary angles of projection is 50 m and 30 m respectively. The initial speed of projectile is

1. $10\sqrt{34}$ m/s
2. 40 m/s
3. 20 m/s
4. 10 m/s

Q. A body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at times $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is the acceleration due to gravity)

1. $\frac{g(t_2-t_1{)}^2}{8}$
2. $\frac{g(t_1+t_2{)}^2}{4}$
3. $\frac{g(t_1+t_2{)}^2}{8}$
4. $\frac{g(t_2-t_1{)}^2}{4}$

Q. A particle of mass m is projected with velocity v making an angle of ${45}^{\circ }$ with the horizontal. The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is (where g = acceleration due to gravity)

1. $Zero$
2. $\frac{m{v}^3}{\left(4\sqrt{2}g\right)}$
3. $\frac{m{v}^3}{\left(\sqrt{2}g\right)}$
4. $\frac{m{v}^2}{2g}$

Q.

If time of flight of a projectile is 10 seconds. Range is 500 meters. The maximum height attained by it will be

1. 125 m

2. 50 m

3. 100 m

4. 150 m

Q. A ball is projected with kinetic energy E at an angle of ${45}^{\circ }$ to the horizontal. At the highest point during its flight, its kinetic energy will be

1. $Zero$
2. $\frac{E}{2}$
3. $\frac{E}{\sqrt{2}}$
4. $E$

Q. A ball is projected from the ground with velocity $v$ such that its range is maximum. Match Column I entries with the correct entries in Column II.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i.Velocity at half of the maximum height}& a.\sqrt{2}v\\ \text{ii.Velocity at the maximum height}& b.\sqrt{3}v/2\\ \text{iii. Change in velocity when its returns to the ground}& c.\frac{v}{\sqrt{2}}\\ \text{iv. Average velocity when its reaches the maximum height}& d.\frac{v}{2}\sqrt{\frac{5}{2}}\end{array}$

1. i – b ii – c iii – a iv – d
2. i – a ii – c iii – d iv – b
3. i – b ii – a iii – c iv – d
4. i – a ii – c iii –b iv – d

Q.

If the initial velocity of a projectile be doubled, keeping the angle of projection same, the maximum height reached by it will

1. Remain the same

2. Be doubled

3. Be quadrupled

4. Be halved

Q.

Two equal masses (m) are projected at the same angle $\left(\theta \right)$ from two points separated by their range with equal velocities (v). The total momentum at the point of their collision is

1. $\left(Zero\right)$

2. $2mvcos\theta$

3. $-2mvcos\theta$

4. $Noneofthese$