Definition of a Projectile

Q.

The figure shows two positions A and B at the same height h above the ground. If the maximum height of the projectile is H, then determine the time t elapsed between the positions A and B in terms of H.

1. $\sqrt{\frac{4}{g}(H-h)}$

2. $\sqrt{\frac{2}{g}(H-h)}$

3. $\sqrt{\frac{8}{g}(H-h)}$

4. $\sqrt{\frac{6}{g}(H-h)}$

Q.

The initial velocity of a projectile of mass 1 kg is given by $u=(\hat{i}+\sqrt{3}\hat{j})m/s$. What is the time of flight?

1. $\frac{2\sqrt{3}}{5}s$

2. $\frac{\sqrt{3}}{10}s$

3. $\frac{3\sqrt{3}}{5}s$

4. $\frac{\sqrt{3}}{5}s$

Q. A missile was thrown from the top of the Himalayas to Kanyakumari. In absence of air resistance, this motion can be best categorized as .

1. 1D motion
2. 2D motion
3. 3D motion

Q.
A particle is projected from ground as shown. It is at point A at time $t_1$, at point B at time $t_2$, at point C at time $t_3$ & at time $t_4$ it is at D then

1. $\overrightarrow{V_B}-\overrightarrow{V_A}=\overrightarrow{V_D}-\overrightarrow{V_C}$
2. $\frac{\overrightarrow{V_A}}{t_1}=\frac{\overrightarrow{V_B}}{t_2}=\frac{\overrightarrow{V_C}}{t_3}=\frac{\overrightarrow{V_D}}{t_4}$
3. $\frac{\overrightarrow{V_B}-\overrightarrow{V_A}}{t_2-t_1}=\frac{\overrightarrow{V_D}-\overrightarrow{V_C}}{t_4-t_3}$
4. $\frac{\overrightarrow{V_A}+\overrightarrow{V_B}}{2}=\frac{\overrightarrow{V_C}+\overrightarrow{V_D}}{2}$

Q. A particle is projected with initial velocity $\overrightarrow{v}=3\hat{i}+4\hat{j}+12\hat{k}$ & $\overrightarrow{a}$ = $8\hat{i}+6\hat{j}-4\hat{k}$ then path of particle is

1. parabolic
2. not defined as vector in 3D
3. curved but not parabolic
4. straight line

Q. In the given figure for a projectile

1. $y=\left[\frac{x_1{x}_2}{x_1-x_2}\right]tan\theta$
2. $y=\left[\frac{x_1{x}_2}{x_1+x_2}\right]tan\theta$
3. $y=\left[\frac{2x_1{x}_2}{x_1+x_2}\right]cos\theta$
4. $y=\left[\frac{2x_1{x}_2}{x_1+x_2}\right]tan\theta$

Q. If the time of flight of a projectile is doubled, what happens to the maximum height attained?

1. Doubled
2. Halved
3. Remains unchanged
4. Becomes four times

Q. Assertion :The projectile has only vertical component of velocity at the highest point of its trajectory. Reason: At the highest point only one component of velocity is present.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. A projectile is fired from the top of a $40m$ hight cliff with an initial speed of $50m/s$ at an unknown angle. Find its speed when it hits the ground.

Q. An object is projected from ground with speed $20m/s$ at angle ${30}^o$ with horizontal. Its centripetal acceleration one second after the projection is [Take $g=10m/s^2$]

1. $10m/s^2$
2. $zero$
3. $5m/s^2$
4. $12m/s^2$