Motion Under Gravity

When a ruler falls vertically, 5 different persons catch it with different reaction times. ( $g = 9.8\text{ m s}^{-2}$)

A. Person A has reaction time of 0.20 s.

B. Person $B$ has reaction time of 0.22 s.

C. Person C has reaction time of 0.18 s.

D. Person D has reaction time of 0.19 s.

E. Person E has reaction time of 0.21 s.

What is the correct order of the distance travelled by the ruler for each person?

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 $g = 10\text{ m/s}^2$ and neglect the air resistance)

A stone falls from the top of a tower of height $100$ m and at the same time another stone is projected vertically upwards from the ground with a velocity $25$ m/s. The two stones meet after

The following plots show variation of velocity $(v)$ with time $(t)$ of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct?

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts decelerating with $3\text{ m/s}^2$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is $5\text{ m/s}$. The initial height of the airplane is ______ m.

$(g = 10\text{ m/s}^2)$

A juggler throws balls into air. He throws one ball whenever the previous one is at its highest point. If he throws 4 balls in one second, the height from which each ball returns is nearly [acceleration due to gravity is $9.8$ m/s${}^{2}$]

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.

$(g = 10\text{ m/s}^2)$

A gas balloon is going up with a constant velocity of $10\text{ m/s}$. 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 $g = 10\text{ m/s}^2$)

A ball is released from height 'h' which makes perfectly elastic collision with ground. The frequency of periodic vibratory motion is (g=acceleration due to gravity)

A boy throws a ball vertically upwards from a bridge with velocity $5\text{ m/s}$. It strikes water surface after 2 s. The height of the bridge is (Take $g = 10\text{ m/s}^2$)

A ball is released from the top of a tower of height Hm. It takes T second to reach the ground. The height of the ball from the ground after $\frac{T}{4}$ second is

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

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:

A body is released from the top of a tower '$H$' metre high. It takes $t$ second to reach the ground. The height of the body $\frac{t}{2}$ second after release is

A ball is thrown vertically upward with an initial velocity of $150\text{ m/s}$. The ratio of velocity after $3\text{ s}$ and $5\text{ s}$ is $\frac{x+1}{x}$. The value of $x$ is ___________.

$\{$ take, $g = 10\text{ m/s}^2\}$

A small steel ball is dropped from a height of $1.5\text{ m}$ into a glycerine jar. The ball reaches the bottom of the jar $1.5\text{ s}$ after it was dropped. If the retardation is $2.66\text{ m/s}^2$, the height of the glycerine in the jar is about (acceleration due to gravity $g = 9.8\text{ m/s}^2$)

A ball is projected vertically upwards from ground. It reaches a height '$h$' in time $t_1$, continues its motion and then takes a time $t_2$ to reach ground. The height $h$ in terms of $g, t_1$ and $t_2$ is $(g =$ acceleration due to gravity)

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ___________ ms $-2$.

(Given g = 10 ms $-2$)

The ratio of the distances travelled by a freely falling body in the 1st, 2nd, 3rd and 4th second

An NCC parade is going at a uniform speed of $9\text{ km/h}$ under a mango tree on which a monkey is sitting at a height of $19.6\text{ m}$. 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 $g = 9.8\text{ m/s}^2$)

A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ________ m. [Use g = 10 m/s2]

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ____________ s.

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 $t_2$.

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

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 $\frac{h}{3}$ while going up and coming down respectively.

A ball is thrown vertically upwards with a velocity of $19.6\text{ ms}^{-1}$ from the top of a tower. The ball strikes the ground after $6\text{ s}$. The height from the ground up to which the ball can rise will be $\left(\frac{k}{5}\right)\text{ m}$. The value of $k$ is __________. (use $g = 9.8\text{ m/s}^2$)

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

A ball is projected vertically upward with an initial velocity of 50 ms${}^{-1}$ at t = 0s. At t = 2s, another ball is projected vertically upward with same velocity. At t = __________ s, second ball will meet the first ball (g = 10 ms${}^{-2}$).

A bullet is shot vertically downwards with an initial velocity of $100\text{ m/s}$ from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time $t = 20\text{ s}$ will be:

(Take g = 10 m/s2).

A body at rest falls through a height 'h' with velocity 'V'. If it has to fall down further for its velocity to become three times, the distance travelled in that interval is

A student is throwing balls vertically upwards such that he throws the $2$nd ball when the $1$st ball reaches maximum height. If he throws balls at an interval of 3 second, the maximum height of the balls is $\left(g = 10\,\frac{\text{m}}{\text{s}^2}\right)$

Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 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.

A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is:

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap? (Take g = 9.8 m/s2)

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 $\frac{h}{3}$ in both the directions.

Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3s with the same initial velocity of 35 m/s, then these balls collide at a height of ............... m. (Take g = 10 m/s2)

A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around:

(take the value of g as 10 m/s2)

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms${}^{-2}$)

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: (g = 10 m/s2)

A person sitting in the ground floor of a building notices through the window, of height 1.5 m, a ball dropped from the roof of the building crosses the window in 0.1 s. What is the velocity of the ball when it is at the topmost point of the window? ($g = 10\text{ m/s}^2$)

A ball is dropped from the top of a 100 m high tower on a planet. In the last $\frac{1}{2}\text{ s}$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in ms–2) near the surface on that planet is _____.

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to:

[g is the acceleration due to gravity]

______

A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height $\frac{h}{2}$. The velocity versus height of the ball during its motion may be represented graphically by:

(graph are drawn schematically and on not to scale)

A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time $t_1$ if the elevator is at rest and in time $t_2$ if the elevator is moving uniformly. Then

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

Two stones are thrown up simultaneously from the edge of a cliff $240\text{ m}$ high with initial speed of $10\text{ m/s}$ and $40\text{ m/s}$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first?

(Assume stones do not rebound after hitting the ground and neglect air resistance, take $g = 10\text{ m/s}^2$)

(The figures are schematic and not drawn to scale)

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is

A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 m s${}^{-2}$, the velocity with which it hits the ground is

A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v?

(Take g = 10 m/s2)

Consider a rubber ball freely falling from a height $h = 4.9\text{ m}$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be:

Two bodies A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise?

(Take g = 10 m/s2.)

A parachutist after bailing out falls $50\text{ m}$ without friction. When parachute opens, it decelerates at $2\text{ m/s}^2.$ He reaches the ground with a speed of $3\text{ m/s}$. At what height, did he bail out?

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in $\frac{T}{3}$ seconds?

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given g = 9.8 m/s2)

If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the same speed ). If vA and vB are their respective velocities on reaching the ground, then

A particle is thrown vertically upward. Its velocity at half of the height is 10 m/s, then the maximum height attained by it (g = 10 m/s2)

A body dropped from a height $h$ with initial velocity zero, strikes the ground with a velocity 3 m/s. Another body of same mass dropped from the same height $h$ with an initial velocity of 4 m/s. The final velocity of second mass, with which it strikes the ground is

The water drop falls at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at instant the first drop touches the ground. How far above the ground is the second drop at that instant?

A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is ($g = 10\text{ m/s}^2$)

What will be the ratio of the distance moved by a freely falling body from rest in 4th and 5th seconds of journey?