Time of Flight

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

Q. A stone thrown from a point on the ground at ${30}^{\circ }$ to the horizontal to hit another point on the ground $145\text{m}$ away, fell short by $5\text{m}$. A second trial at a different angle (but the same speed) again fell short by the same distance. What was the difference in their flight times ?

1. $5\text{s}$
2. $4\text{s}$
3. $3\text{s}$
4. $8\text{s}$

Q.

A particle is thrown with velocity u at an angle $\alpha$ from the horizontal. Another particle is thrown with the same velocity at an angle $\alpha$ from the vertical. The ratio of times of flight of two particles will be

1. $tan2\alpha :1$

2. $cot2\alpha :1$

3. $tan\alpha :1$

4. $cot\alpha :1$

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. $0\%$

2. $1\%$

3. $9\%$

4. $11\%$

Q. A projectile is thrown from the ground with an initial velocity of $(4\hat{i}+3\hat{j})$$m/s$. It reaches its greatest height above the ground after (Take $g=10m/s^2$)

1. $0.20s$
2. $0.30s$
3. $0.45s$
4. $4.5s$

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

Q.

A ball is projected upwards from the top of tower with a velocity $50m{s}^{-1}$ making angle ${30}^{\circ }$ with the horizontal. The height of the tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground

1. 2.33 sec

2. 5.33 sec

3. 7.11 sec

4. 6.33 sec

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 stone is projected at an angle ${45}^{\circ }$ to the horizontal with a velocity $12\sqrt{g}$, where $g$ is acceleration due to gravity at the place. It just passes over a wall $27\text{m}$ high, at a horizontal distance of $108\text{m}$ from the point of projection. Take $g=10{\text{ms}}^{-2}$

1. The stone passes over the wall during ascent.
2. The stone passes over the wall during descent.
3. The difference in velocity at the initial and final point on ground is zero.
4. The difference in speed at the initial and final point on ground is zero.

Q. Two stones $A$ and $B$ are projected from the same point. $B$ is thrown $1$ second after $A$ is thrown. $A$ is projected with a velocity of $60m/s$ at an angle ${30}^{\circ }$ with the horizontal and $B$ is projected with velocity $u$ at an angle of ${45}^{\circ }$ with the horizontal. Find $u$ if both stones hit the ground at the same time. (Take $g=10m/s$)

1. $25m/s$
2. $25\sqrt{2}m/s$
3. $25\sqrt{3}m/s$
4. $\frac{25}{2}m/s$

Q. On seeing enemy ships at a distance of 125 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 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 = 5s, H = 31.25 m

2. T = 5s, H = 45.6 m

3. T = 11s, H = 31.25 m

4. T = 10s, H = 45.1 m

Q.

A particle is thrown with velocity u at an angle $\alpha$ from the horizontal. Another particle is thrown with the same velocity at an angle $\alpha$ from the vertical. The ratio of times of flight of two particles will be

1. $tan2\alpha :1$

2. $cot2\alpha :1$

3. $tan\alpha :1$

4. $cot\alpha :1$

Q. Two stones $A$ and $B$ are projected from the same point. $B$ is thrown $1$ second after $A$ is thrown. $A$ is projected with a velocity of $60m/s$ at an angle ${30}^{\circ }$ with the horizontal and $B$ is projected with velocity $u$ at an angle of ${45}^{\circ }$ with the horizontal. Find $u$ if both stones hit the ground at the same time. (Take $g=10m/s$)

1. $25m/s$
2. $25\sqrt{2}m/s$
3. $25\sqrt{3}m/s$
4. $\frac{25}{2}m/s$