Motion in a Straight Line Set-1

Question 1

A ball is released from a height $h$. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$. [(JEE Main 2022)]

Accepted Answer

$t_2 = (\sqrt{2} - 1) t_1$

Answer

$t_1 = (\sqrt{2}) t_2$

Answer

$t_1 = (\sqrt{2} - 1) t_2$

Answer

$t_2 = (\sqrt{2} + 1) t_1$

Question 2

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws $n$ balls per second, the maximum height the balls can reach is [(JEE Main 2022)]

Accepted Answer

$g / 2 n^2$

Answer

$g / 2 n$

Answer

$g / n$

Answer

$2 g n$

Question 3

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height $h$. Find the ratio of the times in which it is at height $h / 3$ while going up and coming down respectively. [(JEE Main 2022)]

Accepted Answer

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

Answer

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

Answer

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

Answer

$1/3$

Question 4

At time $t=0$ a particle starts travelling from a height $7 \ \mathrm{m}$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $\hat{i}$ and $\hat{j}$ directions are defined as $3t$ and $5t^3$ respectively. At $t = 1 \ \mathrm{s}$ acceleration of the particle will be [(JEE Main 2022)]

Accepted Answer

$30 \hat{j}$

Answer

$-30 \hat{j}$

Answer

$3 \hat{i} + 15 \hat{j}$

Answer

$15 \hat{j}$

Question 5

A NCC parade is going at a uniform speed of $9 \ \mathrm{km/h}$ under a mango tree on which a monkey is sitting at a height of $19.6 \ \mathrm{m}$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given $g=9.8 \ \mathrm{m/s}^2$) [(JEE Main 2022)]

Accepted Answer

5 m

Answer

10 m

Answer

19.8 m

Answer

24.5 m

Question 6

A bullet is shot vertically downwards with an initial velocity of $100 \ \mathrm{m/s}$ from a certain height. Within $10 \ \mathrm{s}$, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time $t = 20 \ \mathrm{s}$ will be: (Take $g = 10 \ \mathrm{m/s}^2$) [(JEE Main 2022)]

Accepted Answer

Graph (a)

Answer

Graph (b)

Answer

Graph (c)

Answer

Graph (d)

Question 7

Two projectiles are thrown with same initial velocity making an angle of $45^\circ$ and $30^\circ$ with the horizontal respectively. The ratio of their respective ranges will be : [(JEE Main 2022)]

Accepted Answer

$2 : \sqrt{3}$

Answer

$1 : \sqrt{2}$

Answer

$\sqrt{2} : 1$

Answer

$\sqrt{3} : 2$

Question 8

Two projectiles thrown at $30^\circ$ and $45^\circ$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is : [(JEE Main 2022)]

Accepted Answer

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

Answer

$1:2$

Answer

$2:1$

Answer

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

Question 9

A ball is projected from the ground with a speed $15 \ \mathrm{ms}^{-1}$ at an angle $	heta$ with horizontal so that its range and maximum height are equal, then '$	an 	heta$' will be equal to : [(JEE Main 2022)]

Accepted Answer

4

Answer

$1 / 4$

Answer

$1 / 2$

Answer

2

Question 10

Two projectiles $P_1$ and $P_2$ thrown with speed in the ratio $\sqrt{3} : \sqrt{2}$, attain the same height during their motion. If $P_2$ is thrown at an angle of $60^\circ$ with the horizontal, the angle of projection of $P_1$ with horizontal will be : [(JEE Main 2022)]

Accepted Answer

$45^\circ$

Answer

$15^\circ$

Answer

$30^\circ$

Answer

$60^\circ$

Question 11

A projectile is projected with velocity of $25 \ \mathrm{m/s}$ at an angle $	heta$ with the horizontal. After $t$ seconds its inclination with horizontal becomes zero. If $R$ represents horizontal range of the projectile, the value of $	heta$ will be : [use $g = 10 \ \mathrm{m/s}^2$] [(JEE Main 2022)]

Accepted Answer

$\frac{1}{5}$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{3}$

Answer

$\frac{1}{4}$

Question 12

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $X_P(t) = \alpha t + \beta t^2$ and $X_Q(t) = f t - t^2$. At what time, both the buses have same velocity? [(JEE Main 2022)]

Accepted Answer

$\frac{f - \alpha}{2 (\beta + 1)}$

Answer

$\frac{f + \alpha}{\beta + 1}$

Answer

$\frac{\alpha + f}{2 (\beta - 1)}$

Question 13

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. [(JEE Main 2022)]
Assertion A : Two identical balls A and B thrown with same velocity '$u$' at two different 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 said heights $h_1 h_2 = \frac{R^2}{16}$. Choose the correct answer :

Accepted Answer

Both A and R are true and R is the correct explanation of A.

Answer

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

Answer

A is true but R is false.

Answer

A is false but R is true.

Question 14

A girl standing on road holds her umbrella at $45^\circ$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2} \ \mathrm{kmh}^{-1}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is : [(JEE Main 2022)]

Accepted Answer

$30 \sqrt{2} \ \mathrm{kmh}^{-1}$

Answer

$30 \ \mathrm{kmh}^{-1}$

Answer

$25 \sqrt{2} \ \mathrm{kmh}^{-1}$

Answer

$25 \ \mathrm{kmh}^{-1}$

Question 15

A projectile is launched at an angle '$\alpha$' with the horizontal with a velocity $20 \ \mathrm{ms}^{-1}$. After $10 \ \mathrm{s}$, its inclination with horizontal is '$\beta$'. The value of $	an \beta$ will be : ($g = 10 \ \mathrm{ms}^{-2}$). [(JEE Main 2022)]

Accepted Answer

$	an \alpha - 5 \sec \alpha$

Answer

$	an \alpha + 5 \sec \alpha$

Answer

$2 	an \alpha - 5 \sec \alpha$

Answer

$2 	an \alpha + 5 \sec \alpha$

Question 16

Velocity $(v)$ and acceleration $(a)$ in two systems of units 1 and 2 are related as $v_2 = v_1 / m$ and $a_2 = a_1 / mn$ respectively. Here $m$ and $n$ are constants. The relations for distance and time in two systems respectively are : [(JEE Main 2022)]

Accepted Answer

$L_2 = \frac{L_1}{n}$ and $T_2 = \frac{T_1}{m}$

Answer

$L_2 = \frac{L_1}{n^2}$ and $T_2 = \frac{T_1}{m}$

Answer

$L_2 = \frac{L_1}{m}$ and $T_2 = \frac{T_1}{n}$

Answer

$L_2 = \frac{L_1}{m}$ and $T_2 = \frac{T_1}{n^2}$

Question 17

A person can throw a ball upto a maximum range of $100 \ \mathrm{m}$. How high above the ground he can throw the same ball? [(JEE Main 2022)]

Accepted Answer

50 m

Answer

25 m

Answer

100 m

Answer

200 m

Question 18

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of $10 \ \mathrm{m}$ in $t \ \mathrm{s}$, the distance travelled by the toy in the next $t \ \mathrm{s}$ will be : [(JEE Main 2022)]

Accepted Answer

30 m

Answer

10 m

Answer

20 m

Answer

40 m

Question 19

Two balls A and B are placed at the top of $180 \ \mathrm{m}$ tall tower. Ball A is released from the top at $t = 0 \ \mathrm{s}$. Ball B is thrown vertically down with an initial velocity '$u$' at $t = 2 \ \mathrm{s}$. After a certain time, both balls meet $100 \ \mathrm{m}$ above the ground. Find the value of '$u$' in $\mathrm{ms}^{-1}$. [use $g = 10 \ \mathrm{ms}^{-2}$] : [(JEE Main 2022)]

Accepted Answer

30

Answer

10

Answer

15

Answer

20

Question 20

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^\circ$ and $48^\circ$ with the horizontal are $R_1, R_2$ and $H_1, H_2$ respectively. Choose the correct option : [(JEE Main 2021)]

Accepted Answer

$R_1 = R_2$ and $H_1 < H_2$

Answer

$R_1 > R_2$ and $H_1 = H_2$

Answer

$R_1 < R_2$ and $H_1 < H_2$

Answer

$R_1 = R_2$ and $H_1 = H_2$

Question 21

A helicopter is flying horizontally with a speed '$v$' at an altitude '$h$' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped? [(JEE Main 2021)]

Accepted Answer

$\sqrt{h^2 + \frac{2 h v^2}{g}}$

Answer

$v \sqrt{\frac{2 h}{g}}$

Answer

$\sqrt{h^2 - \frac{2 h v^2}{g}}$

Answer

$\sqrt{h^2 - \frac{4 h v^2}{g}}$

Question 22

A player kicks a football with an initial speed of $25 \ \mathrm{ms}^{-1}$ at an angle of $45^\circ$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take $g = 10 \ \mathrm{ms}^{-2}$) [(JEE Main 2021)]

Accepted Answer

$h_{max} = 15.625 \ \mathrm{m}, T = 1.77 \ \mathrm{s}$

Answer

$h_{max} = 10 \ \mathrm{m}, T = 2.5 \ \mathrm{s}$

Answer

$h_{max} = 15.625 \ \mathrm{m}, T = 3.54 \ \mathrm{s}$

Answer

$h_{max} = 3.54 \ \mathrm{m}, T = 0.125 \ \mathrm{s}$

Question 23

Water drops are falling from a nozzle of a shower onto the floor, from a height of $9.8 \ \mathrm{m}$. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor. [(JEE Main 2021)]

Accepted Answer

7.35 m

Answer

4.18 m

Answer

2.94 m

Answer

2.45 m

Question 24

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a : [(JEE Main 2021)]

Accepted Answer

straight line vertically down the plane

Answer

hyperbola

Answer

parabola in the direction of motion of plane

Answer

parabola in a direction opposite to the motion of plane

Question 25

A ball is thrown up with a certain velocity so that it reaches a height '$h$'. Find the ratio of the two different times of the ball reaching $h / 3$ in both the directions. [(JEE Main 2021)]

Accepted Answer

$\frac{\sqrt{h}}{\sqrt{h - h/3}}$

Answer

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

Answer

$1/3$

Answer

$\frac{\sqrt{h}}{\sqrt{2 h/3}}$

Question 26

The instantaneous velocity of a particle moving in a straight line is given as $V = \alpha t + \beta t^2$, where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between $1 \ \mathrm{s}$ and $2 \ \mathrm{s}$ is : [(JEE Main 2021)]

Accepted Answer

$\frac{3}{2} \alpha + \frac{7}{3} \beta$

Answer

$3 \alpha + 7 \beta$

Answer

$\alpha / 2 + \beta / 3$

Answer

$\frac{3}{2} \alpha + \frac{7}{2} \beta$

Question 27

A balloon was moving upwards with a uniform velocity of $10 \ \mathrm{m/s}$. An object of finite mass is dropped from the balloon when it was at a height of $75 \ \mathrm{m}$ from the ground level. The height of the balloon from the ground when object strikes the ground was around : (takes the value of $g$ as $10 \ \mathrm{m/s}^2$) [(JEE Main 2021)]

Accepted Answer

125 m

Answer

300 m

Answer

200 m

Answer

250 m

Question 28

The relation between time $t$ and distance $x$ for a moving body is given as $t = m x^2 + n x$, where $m$ and $n$ are constants. The retardation of the motion is : (When $v$ stands for velocity) [(JEE Main 2021)]

Accepted Answer

$2 m v^3$

Answer

$2 m n v^3$

Answer

$2 n v^3$

Answer

$2 n^2 v^3$

Question 29

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^	ext{th}$ second after its fall to the next droplet is $34.3 \ \mathrm{m}$. At what rate the droplets are coming from the tap ? (Take $g = 9.8 \ \mathrm{m/s}^2$) [(JEE Main 2021)]

Accepted Answer

1 drop / second

Answer

3 drops / 2 seconds

Answer

2 drops / second

Answer

1 drop / 7 seconds

Question 30

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time $t_1$. If he remains stationary on a moving escalator then the escalator takes him up in time $t_2$. The time taken by him to walk up on the moving escalator will be : [(JEE Main 2021)]

Accepted Answer

$\frac{t_1 t_2}{t_1 + t_2}$

Answer

$\frac{t_1 t_2}{t_1 - t_2}$

Answer

$\frac{t_1 t_2}{t_2 - t_1}$

Answer

$t_2 - t_1$

Question 31

A butterfly is flying with a velocity $4\sqrt{2} \ \mathrm{m/s}$ in North-East direction. Wind is slowly blowing at $1 \ \mathrm{m/s}$ from North to South. The resultant displacement of the butterfly in 3 seconds is : [(JEE Main 2021)]

Accepted Answer

$15 \ \mathrm{m}$

Answer

$12\sqrt{2} \ \mathrm{m}$

Answer

$20 \ \mathrm{m}$

Answer

$3 \ \mathrm{m}$

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