Time of Flight

Q. On seeing enemy ships at a distance of $125\text{m}$ from the shore, the canons start firing fireballs. The captain of the ship saw the cannon fire. He knows the velocity of the fireballs is $50\text{m/s}$. Now in how much time does he have to steer his ship in some other direction so as to save his crew. Use angle of projection as ${30}^{\circ }$. Also find the maximum height that the fireball reaches above water.

1. $T=5\text{s},H=31.25\text{m}$

2. $T=5\text{s},H=45.6\text{m}$

3. $T=11\text{s},H=31.25\text{m}$

4. $T=10\text{s},H=45.1\text{m}$

Q. For a given velocity, a projectile has the same range R for two angles of projection if $t_1$ and $t_2$ are the times of flight in the two cases then

1. $t_1{t}_2\propto \frac{1}{R^2}$
2. $t_1{t}_2\propto R^2$
3. $t_1{t}_2\propto R$
4. $t_1{t}_2\propto \frac{1}{R}$

Q. Referring to above question, the angle with the horizontal at which the projectile was projected is

1. $ta{n}^{-1}\left(\frac{3}{4}\right)$
2. $ta{n}^{-1}\left(\frac{4}{3}\right)$
3. $Notobtainablefromthegivendata$
4. $si{n}^{-1}\left(\frac{3}{4}\right)$

Q.

A body is thrown with a velocity of 9.8 m/s making an angle of ${30}^{\circ }$ with the horizontal. It will hit the ground after a time

1. 1.5 s

2. 1 s

3. 3 s

4. 2 s

Q. A body is thrown vertically upwards with velocity u. The distance travelled by it in the fifth and the sixth seconds are equal. The velocity u is given by (g=9.8 m/$s^2)$

1. 98.0 m/s
2. 24.5 m/s
3. 49.0 m/s
4. 73.5 m/s

Q.

A projectile can have the same range R for two angles of projection. If T₁ and T₂ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

1. R²

2. R

3. (1/R)

4. 1/R²

Q.

A ball thrown by a boy is caught by another after 2 sec. some distance away in the same level. If the angle of projection is ${30}^{\circ }$, the velocity of projection is

1. None of these

2. 19.6 m/s

3. 9.8 m/s

4. 14.7 m/s

Q. A football player throws a ball with a velocity of 50 metre/sec at an angle 30 degrees from the horizontal. The ball remains in the air for $(g=10m/s^2)$

1. 5 sec
2. 0.625 sec
3. 2.5 sec
4. 1.25 sec

Q.

If for a given angle of projection, the horizontal range is doubled, the time of flight becomes

1. 

2. 

3. 

4. 

Q.

The friction of the air causes vertical retardation equal to one tenth of the acceleration due to gravity (Take g = $10m{s}^{-2}$). The time of flight will be decreased by

1. 

2. 

3. 

4.