Answer to Question #102181 in Mechanics | Relativity for bjbnl

Question #102181
A projectile of mass 0.5 kg is shot straight up with an initial speed of 18.8 m/s. How much energy is lost from the system if it reaches a max height of 15.9048 meters?
1
Expert's answer
2020-02-07T10:24:15-0500

1). Определим начальную скорость снаряда, при которой он достигнет высоты "h_1=15.9048 m"

To do this, we apply the kinetic energy change theorem

"\\frac{mV^2_{01}}{2}=mgh_1"

where do we get

"V_{01}=\\sqrt{2gh_1}=\\sqrt{2\\cdot 9.81\\cdot 15.9048}=\\sqrt{312.052}=17.665m\/c"

2). Then the energy loss is

"\\Delta E=\\frac{mV^2_{02}}{2}-\\frac{mV^2_{01}}{2}=\\frac{0.5\\cdot 18.8^2}{2}-\\frac{0.5\\cdot 17.665^2}{2}=88.36-78.01=10.35J"


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