Q. 123.9( 78 Votes )

A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

Answer :

Given,


Ball is dropped from a height = 90 m


Time interval, 0 ≤ t ≤ 12


Initial velocity of the ball =0 m/s


Final velocity of the ball = v m/s


Acceleration due to gravity, g = 9.81 ms-2


From 2nd equation of motion for freely falling body,


s = ut + 0.5gt2


where,


u = Initial velocity


g = Acceleration due to gravity


s = Distance covered


t = Time


90 = 0 + (0.5×9.81)t2


t = 4.29 s


From 1st equation of motion for freely falling body,


v = u + gt


where,


v = Final velocity


u = Initial velocity


g = Acceleration due to gravity


t = Time


v = 0 + (9.81×4.29) = 42.04 m/s


Bounce velocity of the ball, vb = 0.9v = 37.84 m/s


Time (t’) by the bouncing ball to reach maximum is given by,


v = vb – gt’


where,


v = Final velocity


vb = Bounce velocity


g = Acceleration due to gravity


t’ = Bouncing time


0 = 37.84 – (9.81×t’)


t’ = 3.86 s


Total time taken by the ball = t + t’ = 4.29 + 3.86 = 8.15 s


The iterations go on like this up to ball reach a static condition.


The graph obtained by the data is,



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Motion in a Straight Line - 10Motion in a Straight Line - 10Motion in a Straight Line - 1063 mins
Motion in a Straight Line - 06Motion in a Straight Line - 06Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 05Motion in a Straight Line - 05Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 03Motion in a Straight Line - 03Motion in a Straight Line - 0372 mins
Understand The Interesting Concept Of Relative velocity in 1- DimensionUnderstand The Interesting Concept Of Relative velocity in 1- DimensionUnderstand The Interesting Concept Of Relative velocity in 1- Dimension44 mins
Motion in a Straight Line - 11Motion in a Straight Line - 11Motion in a Straight Line - 1169 mins
Motion in a Straight Line - 07Motion in a Straight Line - 07Motion in a Straight Line - 0755 mins
Polish Important Concept of Relative VelocityPolish Important Concept of Relative VelocityPolish Important Concept of Relative Velocity61 mins
Motion in a Straight Line - 09Motion in a Straight Line - 09Motion in a Straight Line - 0962 mins
Motion in a Straight Line - 08Motion in a Straight Line - 08Motion in a Straight Line - 0854 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :