Q12 of 28 Page 55

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.

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,



More from this chapter

All 28 →
10

A player throws a ball upwards with an initial speed of 29.4 m/s.

(a) What is the direction of acceleration during the upward motion of the ball?


(b) What are the velocity and acceleration of the ball at the highest point of its motion?


(c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.


(d) To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 ms-2 and neglect air resistance).

 11

Read each statement below carefully and state with reasons and examples, if it is true or false ;

A particle in one-dimensional motion


(a) with zero speed at an instant may have non-zero acceleration at that instant


(b) with zero speed may have non-zero velocity,


(c) with constant speed must have zero acceleration,


(d) with positive value of acceleration must be speeding up.

 13

Explain clearly, with examples, the distinction between:

(a) Magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;


(b) Magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity, consider one-dimensional motion only].

 14

A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km/h. What is the

(a) Magnitude of average velocity, and


(b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min ?


[Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero!]