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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.

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As an experienced tutor registered on UrbanPro, I understand the importance of clear and concise explanations, especially when it comes to illustrating concepts through graphs. UrbanPro is indeed a fantastic platform for connecting with students and providing top-notch online coaching and tuition services. Now,...
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As an experienced tutor registered on UrbanPro, I understand the importance of clear and concise explanations, especially when it comes to illustrating concepts through graphs. UrbanPro is indeed a fantastic platform for connecting with students and providing top-notch online coaching and tuition services.

Now, let's tackle the problem at hand. We have a ball being dropped from a height of 90 meters, and at each collision with the floor, it loses one-tenth of its speed. To plot the speed-time graph of its motion from t=0t=0 to t=12t=12 seconds, we need to break down the problem step by step.

  1. Initial Conditions: At t=0t=0, the ball is dropped from a height of 90 meters, so its initial speed is zero.

  2. Speed after Each Collision: After each collision with the floor, the ball loses one-tenth of its speed. This means the speed decreases by 10% after each collision.

  3. Time Intervals: We need to calculate the speed at different time intervals until t=12t=12 seconds.

Let's calculate the speed at each time interval:

  • At t=0t=0, initial speed v0=0v0=0 m/s.
  • At t=1t=1 second, the ball has fallen for 1 second, so its speed is v1=2ghv1=2gh
  • where g=9.8g=9.8 m/s² and h=90h=90 m.
  • At t=2t=2 seconds, the ball has fallen for 2 seconds from rest, so its speed is v2=0.9×v1v2=0.9×v1.
  • Repeat this process for t=3,4,5,...t=3,4,5,... until t=12t=12 seconds.

Once we have calculated the speed at each time interval, we can plot it on a graph with time on the x-axis and speed on the y-axis. This will give us the speed-time graph of the ball's motion.

If you're interested, I can provide the step-by-step calculations and then help you plot the graph. Let me know if you'd like to proceed!

 
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