A stone is dropped from the top of a tower $500\ m$ high into a pond of water at the base of the tower. When is the splash heard at the top? Given, $g=10\ ms^{-2}$ and speed of sound $=340\ ms^{-1}$.

Given:

A stone is dropped from the top of a tower $500\ m$ high into a pond of water at the base of the tower. 

To do:

To find out when is the splash heard at the top.

Solution:

Height of the tower, $s=500\ m$

Velocity of sound, $v=340\ m/s$

Acceleration due to gravity, $g=10\ m/s^2$

Initial velocity of the stone, $u=0$ $(since\ the\ stone\ is\ initially\ at\ rest)$

Time taken by the stone to fall to the base of the tower, $t_1$

According to the second equation of motion:

$S=ut_1+\frac{1}{2}gt_1^2$

$500=0\times t_1+\frac{1}{2}\times10\times t_1^2$

$t_1^2=100$

$t_1=10\ s$

Now, the time taken by the sound to reach the top from the base of the tower is, $t_2=\frac{500}{340}=1.47\ s$

Therefore, the splash is heard at the top after time, $t$

Where, $t=t_1+t_2=10+1.47=11.47\ s$

Tutorialspoint

Simply Easy Learning

---

Updated on 10-Oct-2022 13:23:18

0 Views

Print Article

• Related Articles
• Sound produced by a thunderstorm is heard $10\ s$ after the lightning is seen. Calculate the approximate distance of the thunder cloud. $(Given\ speed\ of\ sound=340\ ms^{-1})$.
• From the top of a 7 m high building, the angle of the elevation of the top of a tower is $60^{o}$ and the angle of the depression of the foot of the tower is $30^{o}$. Find the height of the tower.
• The angle of elevation of the top of a hill at the foot of a tower is \( 60^{\circ} \) and the angle of elevation of the top of the tower from the foot of the hill is \( 30^{\circ} \). If the tower is \( 50 \mathrm{~m} \) high, what is the height of the hill?
• The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.
• A stone is allowed to fall from the top of a tower $100\ m$ high and at the same time another stone is projected vertically upwards from the ground with a velocity of $25\ m/s$. Calculate when and where the two stones will meet.
• From the top of a building \( 15 \mathrm{~m} \) high the angle of elevation of the top of a tower is found to be \( 30^{\circ} \). From the bottom of the same building, the angle of elevation of the top of the tower is found to be \( 60^{\circ} \). Find the height of the tower and the distance between the tower and building.
• From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20\ m$ high building are $45^o$ and $60^o$ respectively. Find the height of the tower.
• The angles of elevation of the top of a tower from two points at a distance of \( 4 \mathrm{~m} \) and \( 9 \mathrm{~m} \) from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is \( 6 \mathrm{~m} \).
• The angle of elevation of the top of tower, from the point on the ground and at a distance of 30 m from its foot, is 30o. Find the height of tower.
• The angle of elevation of the top of a building from the foot of a tower is $30^o$ and the angle of elevation of the top of the tower from the foot of the building is $60^o$. If the tower is $50\ m$ high, find the height of the building.
• From the top of a $7\ m$ high building, the angle of elevation of the top of a cable tower is $60^o$ and the angle of depression of its foot is $45^o$. Determine the height of the tower.
• From the top of a \( 7 \mathrm{~m} \) high building, the angle of elevation of the top of a cable tower is \( 60^{\circ} \) and the angle of depression of its foot is \( 45^{\circ} . \) Determine the height of the tower.
• From a point on the ground the angles of elevation of the bottom and top of a transmission tower fixed at the top of \( 20 \mathrm{~m} \) high building are \( 45^{\circ} \) and \( 60^{\circ} \) respectively. Find the height of the transimission tower.
• Compare the power at which each of the following is moving upwards against the force of gravity? $(given\ g=10\ ms^{-2})$1. A butterfly of mass $1.0\ g$ that flies upward at a rate of $0.5\ ms^{-1}$.2. A $250\ g$ squirrel climbing up on a tree at a rate of $0.5\ ms^{-1}$.
• PQ is a post of given height a , and A B is a tower at some distance. If \( \alpha \) and \( \beta \) are the angles of elevation of B , the top of the tower, at P and Q respectively. Find the height of the tower and its distance from the post.