(A) Let the total time of flight be $T = t_1 + t_2$. The total time of flight is given by $T = 2u/g$,so $u = g(t_1 + t_2)/2$.The height $h$ at time $t

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) Let the total time of flight be $T = t_1 + t_2$. The total time of flight is given by $T = 2u/g$,so $u = g(t_1 + t_2)/2$.The height $h$ at time $t_1$ is given by the equation of motion: $h = ut_1 - \frac{1}{2}gt_1^2$.Substitute $u = \frac{g(t_1 + t_2)}{2}$ into the equation:$h = \left[ \frac{g(t_1 + t_2)}{2} \right] t_1 - \frac{1}{2}gt_1^2$Simplify the expression:$h = \frac{gt_1^2}{2} + \frac{gt_1t_2}{2} - \frac{gt_1^2}{2}$$h = \frac{gt_1t_2}{2}$Therefore,$t_1t_2 = \frac{2h}{g}$.

Class 11 Physics Motion in Straight Line Motion Under Gravity

Medium

$A$ ball is thrown vertically upwards from the ground $G$ with a speed $u$. It reaches a point $B$ at a height $h$ (lower than the maximum height) after time $t_1$. It returns to the ground after time $t_2$ from the instant it was at $B$ during the upward journey. Then $t_1t_2$ is equal to

A
$2h/g$
B
$h/g$
C
$h/2g$
D
$h/4g$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Motion in Straight Line

Subtopic

Motion Under Gravity

Write the equation of velocity of an object falling freely from height $h$.

Medium

View Solution

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:

MediumAIPMT 2006

View Solution

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

MediumAIPMT 2003

View Solution

$A$ body projected vertically upwards crosses a point twice in its journey at a height $h$ after $t_1$ and $t_2$ seconds. The maximum height reached by the body is

DifficultAP EAMCET 2005

View Solution

$A$ body dropped from a height $h$ with an initial speed zero,strikes the ground with a velocity $3 \ km/h$. Another body of the same mass is dropped from the same height $h$ with an initial speed of $4 \ km/h$. Find the final velocity of the second body with which it strikes the ground in $km/h$.

MediumAIPMT 1996

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ ball is thrown vertically upwards from the ground $G$ with a speed $u$. It reaches a point $B$ at a height $h$ (lower than the maximum height) after time $t_1$. It returns to the ground after time $t_2$ from the instant it was at $B$ during the upward journey. Then $t_1t_2$ is equal to

Similar Questions

Write the equation of velocity of an object falling freely from height $h$.

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:

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

$A$ body projected vertically upwards crosses a point twice in its journey at a height $h$ after $t_1$ and $t_2$ seconds. The maximum height reached by the body is

$A$ body dropped from a height $h$ with an initial speed zero,strikes the ground with a velocity $3 \ km/h$. Another body of the same mass is dropped from the same height $h$ with an initial speed of $4 \ km/h$. Find the final velocity of the second body with which it strikes the ground in $km/h$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module