Today I came across the question below. I thought to write about it explaining how to find the total distance traveled by a bouncing object. Photo by cottonbro: Question: A particle falls from h height and bounces. Prove that the total distance traveled is \(\frac{\left ( 1+e^{2} \right )}{\left ( 1-e^{2} \right )}h \). and the total time is \( \sqrt{\frac{2h}{g}} \cdot \frac{(1+e)}{1-e}\) where e is the elasticity coefficient. we can find the particle's velocity when it hits the ground for the first time using the law of mechanical energy conservation as shown below. \(mgh = \frac{1}{2}mv^{2}\) \(\Rightarrow v = \sqrt{2gh}\) and we can use Newton's law to find out the velocity (v) of the particle when it bounces for the first time. \(e = \frac{v}{\sqrt{2gh}}\) \(\Rightarrow v = e\sqrt{2gh} \) According to this, we can determine the particle's speeds when it hits the ground are in a geometric series as follows. \( e\sqrt{2gh}, e^{2}\sqrt{2gh}, e^3\sqrt{2gh},....\) The n
Photo by Stefan Stefancik Everyone who has studied physics in high school knows the doppler effect. For those who don't, the doppler effect is an effect when there is a relative motion between a source of a wave and an observer. As a result of this relative motion, the wave's frequency differs from the actual frequency (f). This is called the Doppler Effect and the observed frequency(f') can be calculated using the following basic equations. Where V is the speed of the wave in the medium; Vo is the speed of the observer Vs is the speed of the source Now it's time to get into the topic. Some people think that we experience the doppler effect when a source reaches us or leaves us at a constant speed. For instance, they think the change in the sound we experience when a train comes toward us is a result of the doppler effect. This is a half-truth. According to the above basic formula, we can derive a new formula to calculate the observed frequency of the train'