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a ball is dropped from a height of 80m 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 8 s.

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one year ago

```							Ball is dropped from a height, s = 90 mInitial velocity of the ball, u = 0Acceleration, a = g = 9.8 m/s2Final velocity of the ball = vFrom second equation of motion, time (t) taken by the ball to hit the ground can be obtained as:s = ut + (1/2)at290 = 0 + (1/2) × 9.8 t2 t = √18.38  = 4.29 sFrom first equation of motion, final velocity is given as:v = u + at= 0 + 9.8 × 4.29 = 42.04 m/sRebound velocity of the ball, ur = 9v / 10 = 9 × 42.04 / 10 = 37.84 m/sTime (t) taken by the ball to reach maximum height is obtained with the help of first equation of motion as:v = ur + at′0 = 37.84 + (– 9.8) t′t′ = -37.84 / -9.8 = 3.86 sTotal time taken by the ball = t + t′ = 4.29 + 3.86 = 8.15 sAs the time of ascent is equal to the time of descent, the ball takes 3.86 s to strike back on the floor for the second time.The velocity with which the ball rebounds from the floor = 9 × 37.84 / 10 = 34.05 m/sTotal time taken by the ball for second rebound = 8.15 + 3.86 = 12.01 sThe speed-time graph of the ball is represented in the given figure as:
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one year ago
```							it is given that Ball is dropped from a height = 90 mTime interval, 0 to 12 sec Initial velocity of the ball , u =0 m/sAcceleration due to gravity , g = 9.8 m/s² s = ut + 1/2 gt2where, u = Initial velocityg = Acceleration due to gravitys = Distance coveredt = Time⇒ 90 = 0 + 1/2 × 9.8 × t² ⇒ 90 = 4.9t² ⇒ t² = 900/49 ∴ t = 30/7 = 4.28 s From 1st equation of motion for freely falling body,v = u + gtWhere u = 0, g = 9.8 m/s² and t = 4.28s ⇒ v = 0 + (9.8 ×4.28) ≈ 42 m/sBounce velocity of the ball, vb = 0.9v = 37.8 m/sTime (t’) by the bouncing ball to reach maximum is given by,v = vb – gt’where,v = Final velocityvb = Bounce velocityg = Acceleration due to gravityt’ = Bouncing time⇒ 0 = 37.84 – (9.8 ×t’)∴ t’ = 3.86 sTotal time taken by the ball = t + t’ = 4.29 + 3.86 = 8.15 s
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one year ago
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