One-Dimensional Motion in a Vertical Line questions | Motion in a Straight Line jee questions

Q 1 :

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_{1}$ . If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t_{2}$ . Time required to reach the ground, if it is dropped from the top of the tower is [2024]

$\sqrt{t_{1} + t_{2}}$
$\sqrt{t_{1} - t_{2}}$
$\sqrt{t_{2} t_{1}}$
$\sqrt{\frac{t_{1}}{t_{2}}}$

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4

(3)

Using: $s = u t + \frac{1}{2} a t^{2}$

In situation (C): $h = \frac{1}{2} g t_{3}^{2}$ ...(i)

Situation (A): $- h = u t_{1} - \frac{1}{2} g t_{1}^{2}$

$h = - u t_{1} + \frac{1}{2} g t_{1}^{2}$ ...(ii)

Situation (B): $- h = - u t_{2} - \frac{1}{2} g t_{2}^{2}$

$h = u t_{2} + \frac{1}{2} g t_{2}^{2}$ ...(iii)

From equation (ii) and equation (iii): $eq (ii) \times t_{2} + eq (iii) \times t_{1}$

$h t_{2} + h t_{1} = \frac{1}{2} g t_{1}^{2} t_{2} + \frac{1}{2} g t_{2}^{2} t_{1} \Rightarrow h (t_{2} + t_{1}) = \frac{1}{2} g t_{1} t_{2} (t_{2} + t_{1})$

$\Rightarrow h = \frac{1}{2} g t_{1} t_{2}$ ...(iv)

Using (i) and (iv), $\frac{1}{2} g t_{3}^{2} = \frac{1}{2} g t_{1} t_{2} \Rightarrow t_{3} = \sqrt{t_{1} \cdot t_{2}}$

Q 2 :

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is _____ m (use g = 10 ${ms}^{- 2}$ ). [2024]

(45)

From A $\to$ B

$- 80 = - 2 v_{1} - \frac{1}{2} \times 10 \times 2^{2}$

$- 80 = - 2 v_{1} - 20$

$- 60 = - 2 v_{1}$

$v_{1} = 30 m/s$

From O to A

$v^{2} = u^{2} + 2 g s$

$30^{2} = 0 + 2 \times (- 10) \times (- s)$

$900 = 20 s$

$s = 45 m$

Q 3 :

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction) [2023]

Time taken by them to reach the earth’s surface will be independent of the properties of their materials.
Insulating ball will reach the earth’s surface earlier than the metal ball.
Both will reach the earth’s surface simultaneously.
Metal ball will reach the earth’s surface earlier than the insulating ball.

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(2)

Insulating ball will reach the earth’s surface earlier than the metal ball.

Q 4 :

A ball is thrown vertically upward with an initial velocity of $150 m/s$ . The ratio of velocity after $3 s$ and $5 s$ is $\frac{x + 1}{x}$ . The value of $x$ is ______. Take $(g = {10 m/s}^{2})$ . [2023]

6
5
- 5
10

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4

(2)

$\vec{v} = \vec{u} + \vec{a} t$

$V = 150 - 10 t$

$V (3) = 150 - 30 = 120$

$V (5) = 150 - 50 = 100$

$\frac{120}{100} = \frac{x + 1}{x} = \frac{6}{5} \Rightarrow x = 5$

Q 5 :

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts decelerating with 3 $m / s ²$ . At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the airplane is __________ m.
$(g = 10 m / s^{2})$ [2026]

20
62.5
82.5
92.5

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(4)

$A to B$

$x_{1} = \frac{1}{2} \times 10 \times 2^{2} = 20 m$

$V = 0 + 10 \times 2$

$B to C$

$5^{2} = 20^{2} - 2 (3) x_{2}$

$x_{2} = \frac{375}{6}$

$x_{2} = 62.5$

$C to D$

$x_{3} = 10 m$

$H = x_{1} + x_{2} + x_{3} = 92.5$

Q 6 :

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time. The first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ______ m.

$(g = 10 m / s^{2})$ [2026]

3.8
4.0
2.5
4.2

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(4)

$Time to reach ground = \sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 \times 5}{10}} = 1 sec$

$Five drops per second$

$Time between each drop = 0.2 sec$

$Time of fall for 4th drop is 1 - 0.6 = 0.4 sec$

$Height of fall of 4th drop is = \frac{1}{2} \times 10 \times {(0.4)}^{2} = 0.8 m$

$Height from ground = 5 - 0.8 = 4.2 m$

Q 7 :

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ______ m. (Take $g = 10 {m/s}^{2}$ ) [2026]

85
150
129
125

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(4)

$75 = 10 t - 5 t^{2}$

$t^{2} - 2 t - 15 = 0$

$(t - 5) (t + 3) = 0 \Rightarrow t = 5 s$

$d = 10 \times 5 = 50 m$

$height from ground,$

$H = 10 \times 5 + 75 = 125 m$

Q 8 :

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ______ m.

(Take $g = 10 {m/s}^{2}$ and neglect the air resistance) [2026]

(13)

$Distance fallen = 18 - h$

$u = 0$

$using v^{2} = u^{2} + 2 a s$

$v^{2} = 2 g (18 - h)$

$Mag. of velocity = mag. of acceleration$

$v = 10 m/s$

$100 = 2 \times 10 (18 - h)$

$\Rightarrow h = 13 m$

Topic Question Set

Q 2 :

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is _____ m (use g = 10 ${ms}^{- 2}$ ). [2024]

Q 3 :

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction) [2023]

Q 4 :

A ball is thrown vertically upward with an initial velocity of $150 m/s$ . The ratio of velocity after $3 s$ and $5 s$ is $\frac{x + 1}{x}$ . The value of $x$ is ______. Take $(g = {10 m/s}^{2})$ . [2023]

Q 7 :

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ______ m. (Take $g = 10 {m/s}^{2}$ ) [2026]

Q 8 :

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ______ m.

(Take $g = 10 {m/s}^{2}$ and neglect the air resistance) [2026]

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Topic Question Set

Q 2 : A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is _____ m (use g = 10 ms-2). [2024]

Q 3 : Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction) [2023]

Q 4 : A ball is thrown vertically upward with an initial velocity of 150 m/s. The ratio of velocity after 3 s and 5 s is x+1x. The value of x is ______. Take (g=10 m/s2). [2023]

Q 6 : Water drops fall from a tap on the floor, 5 m below, at regular intervals of time. The first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ______ m. (g=10m/s2) [2026]

Q 7 : A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ______ m. (Take g=10 m/s2) [2026]

Q 8 : From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ______ m. (Take g=10 m/s2 and neglect the air resistance) [2026]

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Q 2 :

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is _____ m (use g = 10 ${ms}^{- 2}$ ). [2024]

Q 3 :

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction) [2023]

Q 4 :

A ball is thrown vertically upward with an initial velocity of $150 m/s$ . The ratio of velocity after $3 s$ and $5 s$ is $\frac{x + 1}{x}$ . The value of $x$ is ______. Take $(g = {10 m/s}^{2})$ . [2023]

Q 7 :

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ______ m. (Take $g = 10 {m/s}^{2}$ ) [2026]

Q 8 :

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ______ m.

(Take $g = 10 {m/s}^{2}$ and neglect the air resistance) [2026]