A man runs across the roof, top of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is at a lower height than the first. If his speed is $9\, m/s$. the (horizontal) distance between the two buildings is $10\, m$ and the height difference is $9\, m$, will be able to land on the next building ? $($ Take $g = 10 \,m/s^2)$
A man runs across the roof, top of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is at a lower height than the first. If his speed is $9\, m/s$. the (horizontal) distance between the two buildings is $10\, m$ and the height difference is $9\, m$, will be able to land on the next building ? $($ Take $g = 10 \,m/s^2)$
Given, horizontal speed of the $\operatorname{man}\left(u_{x}\right)=9 \mathrm{~m} / \mathrm{s}$
Horizontal distance between the two buildings, $x=10 \mathrm{~m}$
Height difference between the two buildings, $y=9 \mathrm{~m}$
and $g=10 \mathrm{~m} / \mathrm{s}^{2}$
Let the man jumps from point $\mathrm{A}$ and land on the roof of the next building at point $\mathrm{B}$. Taking motion in vertical direction,
$y=u t+\frac{1}{2} a t^{2}$
$\therefore 9=0 \times t+\frac{1}{2} \times 10 \times t^{2} \quad\left(\because u=u_{v}=0\right)$
$\therefore 9=5 t^{2}$
$t=\sqrt{\frac{9}{5}}=\frac{3}{\sqrt{5}}$
$=9 \times \frac{3}{\sqrt{5}}$
$=\frac{27}{\sqrt{5}} m=12 m$
Similar Questions
In the climax of a movie, the hero jumps from a helicopter and the villain chasing the hero also jumps at the same time from the same level. After sometime when they were at same horizontal level, the villain fires bullet horizontally towards the hero. Both were falling with constant acceleration $2\ m/s^2$ , because of parachute. Assuming the hero to be within the range of bullet, and air resistace force on bullet is negligible. Which of the following is correct
In the climax of a movie, the hero jumps from a helicopter and the villain chasing the hero also jumps at the same time from the same level. After sometime when they were at same horizontal level, the villain fires bullet horizontally towards the hero. Both were falling with constant acceleration $2\ m/s^2$ , because of parachute. Assuming the hero to be within the range of bullet, and air resistace force on bullet is negligible. Which of the following is correct
A body of mass $2\; kg$ has an initial velocity of $3 \;m / s$ along $OE$ and it is subjected to a force of $4$ newtons in $OF$ direction perpendicular to $OE$. The distance of the body from $O$ after $4 \;seconds$ will be
A body of mass $2\; kg$ has an initial velocity of $3 \;m / s$ along $OE$ and it is subjected to a force of $4$ newtons in $OF$ direction perpendicular to $OE$. The distance of the body from $O$ after $4 \;seconds$ will be
A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} m / s$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, $0.5 s$ after the splitting. The other part, $t$ seconds after the splitting, falls to the ground at a distance $x$ meters from the point $O$. The acceleration due to gravity $g =10 m / s ^2$.
($1$) The value of $t$ is. . . . . .
($2$) The value of $x$ is. . . . .
Give the answer or qution ($1$) and ($2$)
A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} m / s$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, $0.5 s$ after the splitting. The other part, $t$ seconds after the splitting, falls to the ground at a distance $x$ meters from the point $O$. The acceleration due to gravity $g =10 m / s ^2$.
($1$) The value of $t$ is. . . . . .
($2$) The value of $x$ is. . . . .
Give the answer or qution ($1$) and ($2$)
- [IIT 2021]
From a balloon moving upwards with a velocity of $12\,ms^{-1}$, a packet is released when it is at a height of $65\, m$ from the ground. The time taken by it to reach the ground is...........$s$ $(g = 10\,ms^{-1})$,
Which of the following is the altitude-time graph for a projectile thrown horizontally from the top of the tower
Which of the following is the altitude-time graph for a projectile thrown horizontally from the top of the tower