3.12 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 data: 

 Initial height, h = 90 m 

 Acceleration due to gravity, g = 9.8 ms2 

 Speed lost at each collision = 1/10 of its speed 

 time interval to be considered: 0 to 12 secs. 

 Step 1: Time to fall from 90 m  

h = ½  gt2 ⇒ 90 = 21 × 9.8 × t2 ⇒ t2 = 9.8180 ≈ 18.37 ⇒ t ≈ 4.29 seconds 

Step 2: Speed before first impact 

v = gt = 9.8 × 4.29 ≈ 42 m/s 

After hitting the floor with 42 m/s, ball rebound with; 

vrebound = 0.9×42 = 37.8m/s 

Step 3: 

 Max height after rebound: 

Use: 

...more

Given data: 

 Initial height, h = 90 m 

 Acceleration due to gravity, g = 9.8 ms2 

 Speed lost at each collision = 1/10 of its speed 

 time interval to be considered: 0 to 12 secs. 

 Step 1: Time to fall from 90 m  

h = ½  gt2 ⇒ 90 = 21 × 9.8 × t2 ⇒ t2 = 9.8180 ≈ 18.37 ⇒ t ≈ 4.29 seconds 

Step 2: Speed before first impact 

v = gt = 9.8 × 4.29 ≈ 42 m/s 

After hitting the floor with 42 m/s, ball rebound with; 

vrebound = 0.9×42 = 37.8m/s 

Step 3: 

 Max height after rebound: 

Use: 

t = g / v = 37.8 / 9.8 ≈ 3.86s 

Again, the ball fall back in time 3.86 s, hitting the ground with 

v = g × 3.86 ≈ 37.8 m/s 

Rebound = 0.9×37.8=34.0 m/s 

 

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<div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="none">Given data:</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="none">&nbsp;Initial height, h = 90 m</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="none">&nbsp;Acceleration due to </span>&lt;a href="https://www.shiksha.com/preparation/physics-ncert-solutions-class-11th-gravitation-4325-ns" target="_blank" rel="noreferrer noopener"&gt;<span lang="EN-US" xml:lang="EN-US" data-contrast="none"><span data-ccp-charstyle="Hyperlink">gravity</span></span>&lt;/a&gt;<span lang="EN-US" xml:lang="EN-US" data-contrast="none">, g = 9.8 ms2</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="none">&nbsp;Speed lost at each </span>&lt;a href="https://www.shiksha.com/preparation/physics-work-energy-and-power-collision-5172-tp" target="_blank" rel="noreferrer noopener"&gt;<span lang="EN-US" xml:lang="EN-US" data-contrast="none"><span data-ccp-charstyle="Hyperlink">collision</span></span>&lt;/a&gt;<span lang="EN-US" xml:lang="EN-US" data-contrast="none"> = 1/10 of its speed</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="none">&nbsp;time interval to be considered: 0 to 12 secs.</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="none">&nbsp;Step 1: Time to fall from 90 m&nbsp;</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">h = ½&nbsp; gt2 ⇒ 90 = 21 × 9.8 × t2 ⇒ t2 = 9.8180 ≈ 18.37 ⇒ t ≈ 4.29 seconds</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">Step 2: Speed before first impact</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">v = gt = 9.8 × 4.29 ≈ 42 m/s</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">After hitting the floor with 42 m/s, ball rebound with;</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">vrebound = 0.9×42 = 37.8m/s</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">Step 3:</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">&nbsp;Max height after rebound:</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">Use:</span><span data-ccp-props="{"134233117":false,"134233118":false,"335559738":240,"335559739":240}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">t = g / v = 37.8 / 9.8 ≈ 3.86s</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">Again, the ball fall back in time 3.86 s, hitting the ground with</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">v = g × 3.86 ≈ 37.8 m/s</span><span data-ccp-props="{}">&nbsp;</span></p></div><div><p><span lang="EN-US" xml:lang="EN-US" data-contrast="auto">Rebound = 0.9×37.8=34.0 m/s</span><span data-ccp-props="{}">&nbsp;</span></p></div><p>&nbsp;</p><div><div><strong><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1729161824phpMrLMUV_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1729161824phpMrLMUV.jpeg" alt="" width="270" height="131"></picture></strong></div></div>

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