Projectile Motion

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A ball whose kinetic energy is $E$ , is projected at an angle of $4 5^{\circ}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

E

(B)

\frac{E}{2}

(C)

\frac{E}{2}

(D)

zero

LEVELJEE Main

A particle is projected at $6 0^{\circ}$ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point is

(A)

K

(B)

zero

(C)

\frac{K}{4}

(D)

\frac{K}{2}

JEE Main 2019, 10 April Shift-II

LEVELJEE Advanced

A plane is inclined at an angle $α = 3 0^{\circ}$ with respect to the horizontal. A particle is projected with a speed $u = 2 ms^{- 1}$ , from the base of the plane, making an angle $θ = 1 5^{\circ}$ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to [Take, $g = 10 ms^{- 2}$ ]

A ball is thrown from a point with a speed $v_{0}$ at an angle of projection $θ$ . From the same point and at the same instant, a person starts running with a constant speed $\frac{v _{0}}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

(A)

Yes,

6 0^{\circ}

(B)

Yes,

3 0^{\circ}

(C)

(D)

Yes,

4 5^{\circ}

JEE Main 2013

LEVELJEE Main

A projectile is given an initial velocity of $(\hat{i} + 2 \hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10 m/s^{2}$ , the equation of its trajectory is

(A)

y = x - 5 x^{2}

(B)

y = 2 x - 5 x^{2}

(C)

4 y = 2 x - 5 x^{2}

(D)

4 y = 2 x - 25 x^{2}

LEVELJEE Main

A boy can throw a stone upto a maximum height of $10 m$ . The maximum horizontal distance that the boy can throw the same stone upto will be

(A)

202 m

(B)

10 m

(C)

102 m

(D)

20 m

JEE Main 2021, 18 March Shift-II

LEVELJEE Main

The projectile motion of a particle of mass $5 g$ is shown in the figure. The initial velocity of the particle is $52 ms^{- 1}$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x \times 1 0^{- 2} kg-ms^{- 1}$ . The value of $x$ to the nearest integer, is ................. .

LEVELJEE Main

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$ , but different maximum heights $h_{1}$ and $h_{2}$ . Which of the following is correct?

(A)

R^{2} = 4 h_{1} h_{2}

(B)

R^{2} = 16 h_{1} h_{2}

(C)

R^{2} = 2 h_{1} h_{2}

(D)

R^{2} = h_{1} h_{2}

LEVELJEE Main

A boy playing on the roof of a $10 m$ high building throws a ball with a speed of $10 m/s$ at an angle of $3 0^{\circ}$ with the horizontal. How far from the throwing point will the ball be at the height of $10 m$ from the ground?\n $[g = 10 m/s^{2}, sin 3 0^{\circ} = \frac{1}{2}, cos 3 0^{\circ} = \frac{3}{2}]$

(A)

5.20 m

(B)

4.33 m

(C)

2.60 m

(D)

8.66 m

LEVELJEE Main

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$ , the total area around the fountain that gets wet is

(A)

π \frac{v ^{4}}{g ^{2}}

(B)

\frac{π}{2} \frac{v ^{4}}{g ^{2}}

(C)

π \frac{v ^{2}}{g ^{2}}

(D)

π \frac{v ^{2}}{g}

JEE Main 2021, 27 Aug Shift-II

LEVELJEE Main

A player kicks a football with an initial speed of $25 ms^{- 1}$ at an angle of $4 5^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take, $g = 10 ms^{- 2}$ )

(A)

h_{max} = 10 m, T = 2.5 s

(B)

h_{max} = 15.625 m, T = 3.54 s

(C)

h_{max} = 15.625 m, T = 1.77 s

(D)

h_{max} = 3.54 m, T = 0.125 s

LEVELJEE Main

A projectile can have the same range $R$ for two angles of projection. If $t_{1}$ and $t_{2}$ are the times of flights in the two cases, then the product of the two times of flights is proportional to

(A)

R^{2}

(B)

\frac{1}{R ^{2}}

(C)

\frac{1}{R}

(D)

R

LEVELJEE Advanced

A body is projected at $t = 0$ with a velocity $10 ms^{- 1}$ at an angle of $6 0^{\circ}$ with the horizontal. The radius of curvature of its trajectory at $t = 1 s$ is $R$ . Neglecting air resistance and taking acceleration due to gravity $g = 10 ms^{- 2}$ , the value of $R$ is

(A)

10.3 m

(B)

2.8 m

(C)

5.1 m

(D)

2.5 m

JEE Main 2021, 1 Sep Shift-II

LEVELJEE Main

The ranges and heights for two projectiles projected with the same initial velocity at angles $4 2^{\circ}$ and $4 8^{\circ}$ with the horizontal are $R_{1}, R_{2}$ and $H_{1}, H_{2}$ , respectively. Choose the correct option.

(A)

R_{1} > R_{2}

and

H_{1} = H_{2}

(B)

R_{1} = R_{2}

and

H_{1} < H_{2}

(C)

R_{1} < R_{2}

and

H_{1} < H_{2}

(D)

R_{1} = R_{2}

and

H_{1} = H_{2}

JEE Main 2019, 12 April Shift-I

LEVELJEE Main

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_{1}$ and $t_{2}$ are the values of the time taken by it to hit the target in two possible ways, the product $t_{1} t_{2}$ is

(A)

\frac{R}{4 g}

(B)

\frac{R}{g}

(C)

\frac{R}{2 g}

(D)

\frac{2 R}{g}

JEE Main 2019, 12 April Shift-I

LEVELJEE Main

The trajectory of a projectile near the surface of the earth is given as $y = 2 x - 9 x^{2}$ . If it were launched at an angle $θ_{0}$ with speed $v_{0}$ , then (Take, $g = 10 ms^{- 2}$ )

(A)

θ_{0} = sin^{- 1} (\frac{1}{5})

and

v_{0} = \frac{5}{3} ms^{- 1}

(B)

θ_{0} = cos^{- 1} (\frac{2}{5})

and

v_{0} = \frac{3}{5} ms^{- 1}

(C)

θ_{0} = cos^{- 1} (\frac{1}{5})

and

v_{0} = \frac{5}{3} ms^{- 1}

(D)

θ_{0} = sin^{- 1} (\frac{2}{5})

and

v_{0} = \frac{3}{5} ms^{- 1}

JEE Main 2019

LEVELJEE Main

Two guns A and B can fire bullets at speeds $1 km/s$ and $2 km/s$ , respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets on the ground fired by the two guns is

(A)

1 : 4

(B)

1 : 16

(C)

1 : 8

(D)

1 : 2

JEE Main 2021, 26 Feb Shift-II

LEVELJEE Main

The trajectory of a projectile in a vertical plane is $y = α x - β x^{2}$ , where $α$ and $β$ are constants and $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $θ$ and the maximum height attained $H$ are respectively given by

(A)

tan^{- 1} α, \frac{α ^{2}}{4 β}

(B)

tan^{- 1} β, \frac{α ^{2}}{2 β}

(C)

tan^{- 1} α, \frac{4 α ^{2}}{β}

(D)

tan^{- 1} (\frac{β}{α}), \frac{α ^{2}}{β}

JEE Advanced 2018

LEVELJEE Advanced

A ball is projected from the ground at an angle of $4 5^{\circ}$ with the horizontal surface. It reaches a maximum height of $120 m$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of $3 0^{\circ}$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is .......... .

JEE Advanced 1986

LEVELJEE Advanced

A body falling freely from a given height $H$ hits an inclined plane in its path at a height $h$ . As a result of this impact the direction of the velocity of the body becomes horizontal. For what value of $(h / H)$ , the body will take maximum time to reach the ground?

JEE Advanced 1996

LEVELJEE Advanced

Two guns situated on the top of a hill of height $10 m$ fire one shot each with the same speed $53 m/s$ at some interval of time. One gun fires horizontally and other fires upwards at an angle of $6 0^{\circ}$ with the horizontal. The shots collide in air at point $P$ ( $g = 10 m/s^{2}$ ). Find (a) the time interval between the firings and (b) the coordinates of the point $P$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x$ - $y$ plane.

JEE Advanced 1997

LEVELJEE Main

The trajectory of a projectile in a vertical plane is $y = a x - b x^{2}$ , where $a, b$ are constants, and $x$ and $y$ are respectively, the horizontal and vertical distances of the projectile from the point of projection. The maximum height attained is ......... and the angle of projection from the horizontal is ......... .

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

A ball dropped on a large inclined plane, bounces repeatedly. Every bounce is perfectly elastic i.e. there is no loss of speed and lines of motion make equal angles with the incline plane before and after the bounce. Find ratio of distance $R_{12}$ between the first and the second bounce to distance $R_{23}$ between the second and the third bounce.

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

From a place on the ground that is 20 m away from a wall, a bullet is fired aiming at a 50 m high mark on the wall. The location of the bullet is shown by a circular dot at some point of time. Where on the wall will the bullet hit?

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

A cylindrical pipe of radius $r$ is rolling towards a frog sitting on the horizontal ground. Centre of the pipe is moving with a constant velocity $v$ . To save itself, the frog jumps off and passes over the pipe touching it only at the top. Denoting air-time of the frog by $T$ , horizontal range of the jump by $R$ and acceleration due to gravity by $g$ , which of the following conclusions can you make?

* Multiple Correct Options

(A)

T = 4 \frac{r}{g}

(B)

T \geq 4 \frac{r}{g}

(C)

R = 4 (g r - v) \frac{r}{g}

(D)

R \geq 4 (g r - v) \frac{r}{g}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A ball whose kinetic energy is E, is projected at an angle of 45∘ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A particle is projected at 60∘ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A projectile is given an initial velocity of (i^+2j^​) m/s, where i^ is along the ground and j^​ is along the vertical. If g=10 m/s2, the equation of its trajectory is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A boy can throw a stone upto a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone upto will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The trajectory of a projectile near the surface of the earth is given as y=2x−9x2. If it were launched at an angle θ0​ with speed v0​, then (Take, g=10 ms−2)

From a place on the ground that is 20 m away from a wall, a bullet is fired aiming at a 50 m high mark on the wall. The location of the bullet is shown by a circular dot at some point of time. Where on the wall will the bullet hit?

A ball whose kinetic energy is $E$ , is projected at an angle of $4 5^{\circ}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

A particle is projected at $6 0^{\circ}$ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point is

A projectile is given an initial velocity of $(\hat{i} + 2 \hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10 m/s^{2}$ , the equation of its trajectory is

A boy can throw a stone upto a maximum height of $10 m$ . The maximum horizontal distance that the boy can throw the same stone upto will be

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$ , the total area around the fountain that gets wet is

The trajectory of a projectile near the surface of the earth is given as $y = 2 x - 9 x^{2}$ . If it were launched at an angle $θ_{0}$ with speed $v_{0}$ , then (Take, $g = 10 ms^{- 2}$ )