A ball is dropped from a bridge of 122.5m above a river.after the ball has been falling for 2sec.a second ball is thrown straigjt down after it.initial velocity of second ball so that both hits the water at same time is?

Question

Answer

Solution:

Given, height of the bridge, h = 122.5 m and time for which the first ball falls, t = 2 s.

Let the initial velocity of the second ball be u.

Calculating the time of flight of the first ball:

We know that the distance travelled by an object falling freely under gravity is given by:

s = ut + 1/2 gt²

Here, u = initial velocity = 0 (since the ball is dropped from rest)

g = acceleration due to gravity = 9.8 m/s²

t = time of flight of the first ball = 2 s

s = height of the bridge = h = 122.5 m

Substituting the values, we get:

h = 1/2 gt²

122.5 = 1/2 × 9.8 × 2²

Therefore, the time of flight of the first ball is:

t = sqrt(122.5/4.9) = sqrt(25) = 5 s

Calculating the distance travelled by the second ball:

The distance travelled by the second ball is also given by:

s = ut + 1/2 gt²

Here, u = initial velocity of the second ball

g = acceleration due to gravity = 9.8 m/s²

t = time of flight of the second ball = 5 - 2 = 3 s (since the second ball is thrown 2 s after the first ball is dropped and both hit the water at the same time)

s = height of the bridge = h = 122.5 m

Substituting the values, we get:

122.5 = ut + 1/2 × 9.8 × 3²

122.5 = ut + 44.1

ut = 122.5 - 44.1 = 78.4

Therefore, the initial velocity of the second ball is:

u = ut/t = 78.4/3 = 26.13 m/s (approx)

Hence, the initial velocity of the second ball should be 26.13 m/s (approx) so that both balls hit the water at the same time.

Answer

Answer:

26.133 m/s

Explanation:

Time taken by first ball to hit water can be found as

s= ut + ½ gt2

122.5 = ½ * 9.8 * t2

t2= 25

t =5

Now the next ball must cover this distance in 3 s to hit water at same time.

122.5 = 3 u + ½ * 9.8 * 32

122.5 = 3u + 44.1

3u = 78.4

u= 26.133 m/s

Similar Class 11 Doubts

A ball is dropped from the top of a tower and 1second later other ball is thrown vertically downward with initial velocity of 15m/s.Find the height of the tower if the two ball strikes the ground simultaneously.?

A particle starts from a point A whose initial velocity is V1 and it reaches with Final velocity V2 at point B which is which is at a distance ' d ' from point A. The path is a straight line. If acceleration is proportional to velocity find the time taken by particle from A to B

A plane is flying horizontally at an altitude of 1960m with a velocity of 50ms jacket is dropped from it find velocity with which packet hits the ground?

An object is dropped vertically down on earth . the change in its speed after falling through a distance d from its highest point is?

Top Courses for Class 11View all

Chemistry Class 11

CUET Mock Test Series

English Class 11

Chemistry Practice Tests: CUET Preparation

CUET Mock Test: Humanities Subjects 2025

Top Courses for Class 11

Top Courses for Class 11

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams