Projectile Motion questions | Projectile Motion jee questions

Q 21 :

A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of 5 ${ms}^{- 1}$ . Neglecting the air resistance, the speed with which the stone hits the ground will be ______ ${ms}^{- 1}$ (given, g = 10 ${ms}^{- 2}$ ). [2023]

20
15
30
25

1

2

3

4

(2)

$v_{y} = \sqrt{2 g h} = \sqrt{200}$

$v_{net} = \sqrt{25 \times 200} = 15 m/s$

Q 22 :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: When a body is projected at an angle 45°, its range is maximum.

Reason R: For maximum range, the value of sin 2θ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below: [2023]

Both A and R are correct but R is NOT the correct explanation of A
Both A and R are correct and R is the correct explanation of A
A is false but R is true
A is true but R is false

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(2)

$R = \frac{u^{2}}{g} \sin 2 θ$

$R is maximum for 2 θ = 90 °$

Q 23 :

Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is $(g = 10 {m/s}^{2})$ [2023]

1 : 1
4 : 9
2 : $\sqrt{3}$
$\sqrt{3}$ : 2

1

2

3

4

(2)

$R_{1} = \frac{u_{1}^{2} \sin 2 θ_{1}}{g}, R_{2} = \frac{u_{2}^{2} \sin 2 θ_{2}}{g}$

$\frac{R_{1}}{R_{2}} = \frac{u_{1}^{2} \sin 2 θ_{1}}{u_{2}^{2} \sin 2 θ_{2}} = \frac{40^{2} \sin (2 \times 30 °)}{60^{2} \sin (2 \times 60 °)} = \frac{4}{9}$

Q 24 :

The trajectory of a projectile, projected from the ground, is given by $y = x - \frac{x^{2}}{20},$ where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be. [2023]

$10 \sqrt{2}$ m
200 m
10 m
5 m

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4

(4)

$y = x - \frac{x^{2}}{20}$

$For maximum height, \frac{d y}{d x} = 0 \to 1 - \frac{2 x}{20} = 0$

$x = 10$

$So, y_{\max} = 10 - \frac{100}{20} = 5 m$

Q 25 :

The range of the projectile projected at an angle of 15° with the horizontal is 50 m. If the projectile is projected with the same velocity at an angle of 45° with the horizontal, then its range will be [2023]

50 m
$50 \sqrt{2}$ m
100 m
$100 \sqrt{2}$ m

1

2

3

4

(3)

$R = \frac{v^{2} \sin 2 θ}{g}$

$R \propto \sin (2 θ)$

$\frac{R_{1}}{R_{2}} = \frac{\sin (2 θ_{1})}{\sin (2 θ_{2})} = \frac{\sin (2 \times 15 °)}{\sin (2 \times 45 °)} = \frac{\sin 30 °}{\sin 90 °}$

$\frac{50}{R_{2}} = \frac{1}{2}$

$R_{2} = 100 m$

Q 26 :

Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is [2023]

2 : $\sqrt{3}$
$\sqrt{3}$ : 1
1 : 3
1 : $\sqrt{3}$

1

2

3

4

(3)

$H_{\max} = \frac{u^{2} \sin^{2} θ}{2 g}$

$\frac{H_{1}}{H_{2}} = \frac{\sin^{2} θ_{1}}{\sin^{2} θ_{2}} = \frac{1}{3}$

Q 27 :

A projectile is projected at $30 °$ from the horizontal with initial velocity $40 {m s}^{- 1}$ . The velocity of the projectile at $t = 2 s$ from the start will be (Given $g = 10 {m/s}^{2}$ ) [2023]

$20 \sqrt{3}$ ${ms}^{- 1}$
$40 \sqrt{3}$ ${ms}^{- 1}$
$20$ ${ms}^{- 1}$
zero

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4

(1)

At $t = 2$ particle is at maximum height moving with velocity $v = 40 \cos 30 ° = 20 \sqrt{3}$ ${ms}^{- 1}$

Q 28 :

Two bodies are projected from ground with same speeds 40 m $s^{- 1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60° with horizontal then sum of the maximum heights, attained by the two projectiles, is ______ m. (Given g = 10 m $s^{- 2}$ ) [2023]

0%

(80)

Since range is same

$\Rightarrow θ_{1} + θ_{2} = 90 °$

$\Rightarrow θ_{2} = 30 °$

$\Rightarrow {(H_{\max})}_{1} + {(H_{\max})}_{2}$ $= \frac{U^{2} \sin^{2} θ_{1}}{2 g} + \frac{U^{2} \sin^{2} θ_{2}}{2 g}$

$= \frac{40^{2}}{20} (\frac{1}{4} + \frac{3}{4}) = 80 m$

Q 29 :

A projectile fired at 30° to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is ______ m $s^{- 1}$ (Given g = 10 m $s^{- 2}$ ) [2023]

0%

(80)

$Time of flight t_{1} + t_{2} = 3 + 5 = 8 sec$

$T = \frac{2 u \sin 30 °}{g}$

$8 = \frac{2 u \sin (30 °)}{10}$

$\Rightarrow u = 80 m/s$

Q 30 :

A boy throws a ball into air at $45 °$ from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then the value of H is _______ m. $(g = 10 {m/s}^{2})$ [2026]

25
15
20
10

1

2

3

4

(2)

Topic Question Set

Q 21 :

A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of 5 ${ms}^{- 1}$ . Neglecting the air resistance, the speed with which the stone hits the ground will be ______ ${ms}^{- 1}$ (given, g = 10 ${ms}^{- 2}$ ). [2023]

Q 23 :

Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is $(g = 10 {m/s}^{2})$ [2023]

Q 24 :

The trajectory of a projectile, projected from the ground, is given by $y = x - \frac{x^{2}}{20},$ where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be. [2023]

Q 25 :

The range of the projectile projected at an angle of 15° with the horizontal is 50 m. If the projectile is projected with the same velocity at an angle of 45° with the horizontal, then its range will be [2023]

Q 26 :

Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is [2023]

Q 27 :

A projectile is projected at $30 °$ from the horizontal with initial velocity $40 {m s}^{- 1}$ . The velocity of the projectile at $t = 2 s$ from the start will be (Given $g = 10 {m/s}^{2}$ ) [2023]

0%

Q 29 :

A projectile fired at 30° to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is ______ m $s^{- 1}$ (Given g = 10 m $s^{- 2}$ ) [2023]

0%

Q 30 :

A boy throws a ball into air at $45 °$ from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then the value of H is _______ m. $(g = 10 {m/s}^{2})$ [2026]

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