The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\)m/s. Its velocity (in m/s) at point \(B\) is:
              

A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H₁. When it is projected with velocity u at an angle $\left(\frac{\pi }{2}-\theta \right)$with the horizontal, it reaches maximum height H₂. The relation between the horizontal range of the projectile R and H₁ & H₂ is: 

An aeroplane is moving with a velocity \(u\). It drops a packet from a height \(h\). The time \(t\) taken by the packet to reach the ground will be:
1. \( \sqrt{\left(\frac{2 g}{h}\right)} \)
2. \( \sqrt{\left(\frac{2 u}{g}\right)} \)
3. \( \sqrt{\left(\frac{h}{2 g}\right)} \)
4. \( \sqrt{\left(\frac{2 h}{g}\right)}\)

The equation of trajectory of a projectile is given by y = x - 10${\mathrm{x}}^2$. Its speed of projection is: (g = 10 m/${\mathrm{s}}^2$)

1. 1 m/s

2. 2 m/s

3. 3 m/s

4. 4 m/s

A particle is thrown obliquely at \(t=0\). The particle has the same K.E. at \(t=5\) seconds and at \(t=9\) seconds. The particle attains maximum altitude at:
1. \(t=6\) s
2. \(t=7\) s
3. \(t=8\) s
4. \(t=14\) s

A body is projected with velocity $\overrightarrow{v}=(\alpha \hat{i}+\beta \hat{j})$ m/s. The time of flight of the body is: [considering x as horizontal and y as vertical axis and g is acceleration due to gravity]

1. $\frac{2\beta }{g}$

2. $\frac{2\alpha }{g}$

3. $\frac{2\alpha \beta }{g}$

4. $\frac{2\alpha }{g\beta }$

When a particle is projected at some angle to the horizontal, it has a range R and time of flight t₁. If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is t₂, then:

1. ${\mathrm{t}}_1+{\mathrm{t}}_2=\frac{2\mathrm{R}}{\mathrm{g}}$

2. ${\mathrm{t}}_1-{\mathrm{t}}_2=\frac{\mathrm{R}}{\mathrm{g}}$

3. ${\mathrm{t}}_1{\mathrm{t}}_2=\frac{2\mathrm{R}}{\mathrm{g}}$

4. ${\mathrm{t}}_1{\mathrm{t}}_2=\frac{\mathrm{R}}{\mathrm{g}}$

Three balls are thrown from the top of a building with equal speeds at different angles. When the balls strike the ground, their speeds are ${\mathrm{v}}_1,{\mathrm{v}}_2$ $\mathrm{and}$ ${\mathrm{v}}_3$ respectively, then:
           

1. ${\mathrm{v}}_1>{\mathrm{v}}_2>{\mathrm{v}}_3$

2. ${\mathrm{v}}_3>{\mathrm{v}}_2={\mathrm{v}}_1$

3. ${\mathrm{v}}_1={\mathrm{v}}_2={\mathrm{v}}_3$

4. ${\mathrm{v}}_1<{\mathrm{v}}_2<{\mathrm{v}}_3$

Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)