Projectile Motion questions | Projectile Motion jee questions

Q 11 :

A projectile is thrown upward at an angle $60 °$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $45 °$ with the horizontal. The initial speed of the projectile is ________ m/s. [2026]

$40$
$20 \sqrt{3}$
$20 \sqrt{2}$
$40 \sqrt{2}$

1

2

3

4

(3)

$u \cos 60 ° = \frac{20}{\sqrt{2}}$

$\frac{u}{2} = \frac{20}{\sqrt{2}}$

$u = \frac{40}{\sqrt{2}}$

$u = 20 \sqrt{2} m/s$

Q 12 :

A ball projected from ground at an angle of $45 °$ just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is:

4.4 m
2.4 m
3.6 m
1.6 m

1

2

3

4

(2)

As ball is projected at an angle $45 °$ to the horizontal therefore Range $= 4 H$

or $10 = 4 H \Rightarrow H = \frac{10}{4} = 2.5 m$

Height of wall $P A = O A \tan θ - \frac{1}{2} \frac{g {(O A)}^{2}}{u^{2} \cos^{2} θ}$

$= 4 - \frac{1}{2} \times \frac{10 \times 16}{10 \times 10 \times \frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}}} = 2.4 m$

Q 13 :

An object of mass $m$ is projected with a momentum $p$ at an angle $θ$ with the horizontal such that its maximum height (H) is half of its Range (R). Minimum kinetic energy of the particle in its path will be

$\frac{p^{2}}{8 m}$
$\frac{3 p^{2}}{4 m}$
$\frac{p^{2}}{10 m}$
$\frac{p^{2}}{5 m}$

1

2

3

4

(3)

$1 \times \frac{1}{2 g} {(\frac{p \sin θ}{m})}^{2} = \frac{p \sin θ}{m g} \times \frac{p \cos θ}{m}$

$\frac{1}{2} \sin^{2} θ = \sin θ \cos θ \Rightarrow \tan θ = 2$

$∴$ $\cos θ = \frac{1}{\sqrt{5}}$

$Minimum kinetic energy = {(\frac{p \cos θ}{2 m})}^{2} = \frac{p^{2}}{2 m} \times \frac{1}{5} = \frac{p^{2}}{10 m}$

Q 14 :

A projectile is fired with velocity $v$ at angle of $θ$ with horizontal. Find the radius of curvature of path at highest point.

$\frac{v^{2} \cos^{2} θ}{g}$
$\frac{v^{2}}{g \cos θ}$
$\frac{v^{2} \cos θ}{g}$
$\frac{v^{2} \cos^{2} θ}{2 g}$

1

2

3

4

(1)

Rate of change of speed is minimum at highest point. Since at highest position.

$R = \frac{{(v \cos θ)}^{2}}{g}$

Q 15 :

Given below are two statements. One is labeled as Assertion A and the other is labeled as Reason R.

Assertion A: Two identical balls A and B thrown with same velocity ‘u’ at two angles with horizontal attained the same range R. If A and B reached the maximum height $h_{1}$ and $h_{2}$ respectively, then $R = 4 \sqrt{h_{1} h_{2}}$

Reason R: product of heights. $h_{1} h_{2} = (\frac{u^{2} \sin^{2} θ}{2 g}) . (\frac{u^{2} \cos^{2} θ}{2 g})$

Choose the CORRECT answer:

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

1

2

3

4

(1)

$We know that if range is same for two angle of projection, then these angle must be complementary.$

$Let first angle of projection be θ then second will be (90 - θ)$

$∴$ $h_{1} = \frac{u^{2} \sin^{2} θ}{2 g} and h_{2} = \frac{u^{2} \sin^{2} (90 - θ)}{2 g} = \frac{u^{2} \cos^{2} θ}{2 g}$

$∴$ $h_{1} h_{2} = \frac{u^{2} \sin^{2} θ}{2 g} \cdot \frac{u^{2} \cos^{2} θ}{2 g}$

$So, reason is correct$

$\Rightarrow \sqrt{h_{1} h_{2}} = \frac{u^{2} \sin θ \cos θ}{2 g}$

$\Rightarrow 4 \sqrt{h_{1} h_{2}} = \frac{4 u^{2} \sin θ \cos θ}{2 g}$

$\Rightarrow 4 \sqrt{h_{1} h_{2}} = \frac{u^{2} (\sin θ \cos θ)}{g}$

$\Rightarrow 4 \sqrt{h_{1} h_{2}} = \frac{u^{2} \sin 2 θ}{g} = R$

$So, assertion is correct and reason is correct explanation of assertion.$

Q 16 :

The two projectiles are projected with the same initial velocities at $15 °$ and $30 °$ with respect to the horizontal. The ratio of their ranges is $1 : x$ . The value of $x$ is [2026]

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

1

2

3

4

(2)

$R \propto \sin (2 θ)$

$\frac{R_{1}}{R_{2}} = \frac{\sin (2 \times 15 °)}{\sin (2 \times 30 °)} = \frac{1 / 2}{\sqrt{3} / 2} = \frac{1}{\sqrt{3}}$

Q 17 :

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and $43.6 t - 4.9 t^{2}$ , respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2 s$ is ________. [2026]

60
45
30
75

1

2

3

4

(2)

$x = 24 t, y = 43.6 t - 4.9 t^{2}$

$v_{x} = \frac{d x}{d t} = 24$

$v_{y} = \frac{d y}{d t} = 43.6 - 9.8 t$

$at t = 2 sec.$

$\tan θ = \frac{v_{y}}{v_{x}} = \frac{24}{24} = 1 \Rightarrow θ = 45 °$

Q 18 :

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ______ m. (Take g = 10 ${m/s}^{2}$ ) [2026]

250
25
500
125

1

2

3

4

(1)

$For range to be same, angle of projection must be complementary angles.$

$T_{1} = \frac{2 u \sin θ}{g} = 10 s,$ $T_{2} = \frac{2 u \cos θ}{g} = 5 s$

$Range = \frac{2 (u \sin θ) (u \cos θ)}{g} = 250 m$

Q 19 :

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______ m/s. (Take g = 10 ${m/s}^{2}$ ) [2026]

(8)

$R_{\max} = \frac{u^{2}}{g}$

$\Rightarrow u^{2} = R_{\max} \times g = 6.4 \times 10 = \frac{64}{10} \times 10$

$\Rightarrow u = \sqrt{64} = 8 m/s$

Topic Question Set

Q 11 :

A projectile is thrown upward at an angle $60 °$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $45 °$ with the horizontal. The initial speed of the projectile is ________ m/s. [2026]

Q 12 :

A ball projected from ground at an angle of $45 °$ just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is:

Q 13 :

An object of mass $m$ is projected with a momentum $p$ at an angle $θ$ with the horizontal such that its maximum height (H) is half of its Range (R). Minimum kinetic energy of the particle in its path will be

Q 14 :

A projectile is fired with velocity $v$ at angle of $θ$ with horizontal. Find the radius of curvature of path at highest point.

Q 16 :

The two projectiles are projected with the same initial velocities at $15 °$ and $30 °$ with respect to the horizontal. The ratio of their ranges is $1 : x$ . The value of $x$ is [2026]

Q 17 :

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and $43.6 t - 4.9 t^{2}$ , respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2 s$ is ________. [2026]

Q 18 :

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ______ m. (Take g = 10 ${m/s}^{2}$ ) [2026]

Q 19 :

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______ m/s. (Take g = 10 ${m/s}^{2}$ ) [2026]

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 11 : A projectile is thrown upward at an angle 60° with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45° with the horizontal. The initial speed of the projectile is ________ m/s. [2026]

Q 12 : A ball projected from ground at an angle of 45° just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is:

Q 13 : An object of mass m is projected with a momentum p at an angle θ with the horizontal such that its maximum height (H) is half of its Range (R). Minimum kinetic energy of the particle in its path will be

Q 14 : A projectile is fired with velocity v at angle of θ with horizontal. Find the radius of curvature of path at highest point.

Q 16 : The two projectiles are projected with the same initial velocities at 15° and 30° with respect to the horizontal. The ratio of their ranges is 1:x. The value of x is [2026]

Q 17 : If x and y coordinates of a projectile as a function of time (t) are given as 24t and 43.6t-4.9t2, respectively, then the angle (in degrees) made by the projectile with horizontal when t=2 s is ________. [2026]

Q 18 : Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ______ m. (Take g = 10 m/s2) [2026]

Q 19 : A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______ m/s. (Take g = 10 m/s2) [2026]

Want Us to Email you About Special Offers & Updates?

Q 11 :

A projectile is thrown upward at an angle $60 °$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $45 °$ with the horizontal. The initial speed of the projectile is ________ m/s. [2026]

Q 12 :

A ball projected from ground at an angle of $45 °$ just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is:

Q 13 :

An object of mass $m$ is projected with a momentum $p$ at an angle $θ$ with the horizontal such that its maximum height (H) is half of its Range (R). Minimum kinetic energy of the particle in its path will be

Q 14 :

A projectile is fired with velocity $v$ at angle of $θ$ with horizontal. Find the radius of curvature of path at highest point.

Q 16 :

The two projectiles are projected with the same initial velocities at $15 °$ and $30 °$ with respect to the horizontal. The ratio of their ranges is $1 : x$ . The value of $x$ is [2026]

Q 17 :

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and $43.6 t - 4.9 t^{2}$ , respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2 s$ is ________. [2026]

Q 18 :

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ______ m. (Take g = 10 ${m/s}^{2}$ ) [2026]

Q 19 :

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______ m/s. (Take g = 10 ${m/s}^{2}$ ) [2026]