Prove that if a body is thrown vertically upward, the time of ascent is equal to the time of descent.
Prove that if a body is thrown vertically upward, the time of ascent is equal to the time of descent.
For upward motion
$v=u-g t$ or $0=u-g t_{1}$
or $t_{1}=\frac{u}{g}$ $....(1)$
For downward motion
$v=u+g t_{2}$ or $v=0+g t_{2}$
As the body falls back to the earth with the same velocity, it was thrown vertically upwards.
$\therefore \quad v=u$
$u=0+g t_{2}$ or $t_{2}=\frac{u}{g}$ $...(2)$
From $(1)+(2)$ the statement is proved.
Similar Questions
Write true or false for the following statements
Motion along a curved line is called translatory or rectilinear motion.
Write true or false for the following statements
Motion along a curved line is called translatory or rectilinear motion.
$(a)$ Derive second equation of motion $S=u t+\frac{1}{2} a t^{2}$ graphically where the symbols have their usual meanings.
$(b)$ A car accelerates uniformly from $18\, km h ^{-1}$ to $36\, km h^{-1}$ in $5$ seconds. Calculate the acceleration and the distance covered by the car in that time.
$(a)$ Derive second equation of motion $S=u t+\frac{1}{2} a t^{2}$ graphically where the symbols have their usual meanings.
$(b)$ A car accelerates uniformly from $18\, km h ^{-1}$ to $36\, km h^{-1}$ in $5$ seconds. Calculate the acceleration and the distance covered by the car in that time.
Two graphs for motion of objects moving along a straight line are shown. State how the speed is changing with time in both cases.
Two graphs for motion of objects moving along a straight line are shown. State how the speed is changing with time in both cases.
A car is moving on a straight road with uniform acceleration. The following table gives the speed of the car at various instants of time.
Time $(s)$
$0$
$10$
$20$
$30$
$40$
$50$
Speed $\left(m s^{-1}\right)$
$5$
$10$
$15$
$20$
$25$
$30$
$(i)$ Draw the speed$-$time graph representing the above set of observations.
$(ii)$ Find the acceleration of the car.
A car is moving on a straight road with uniform acceleration. The following table gives the speed of the car at various instants of time.
| Time $(s)$ | $0$ | $10$ | $20$ | $30$ | $40$ | $50$ |
| Speed $\left(m s^{-1}\right)$ | $5$ | $10$ | $15$ | $20$ | $25$ | $30$ |
$(i)$ Draw the speed$-$time graph representing the above set of observations.
$(ii)$ Find the acceleration of the car.
A piece of stone is thrown vertically upwards. It reaches its maximum height in $3$ second. If the acceleration of the stone be $9.8\, m s ^{-2}$ directed towards the ground, calculate the initial velocity of the stone with which it is thrown upwards. Find the maximum height attained by it.
A piece of stone is thrown vertically upwards. It reaches its maximum height in $3$ second. If the acceleration of the stone be $9.8\, m s ^{-2}$ directed towards the ground, calculate the initial velocity of the stone with which it is thrown upwards. Find the maximum height attained by it.