The kinetic energy of a rocket
"{\\rm KE}=\\frac{mv^2}{2}"So, the initial speed of a rocket
"v=\\sqrt{2{\\rm KE}\/m}=\\sqrt{2\\times 37\/1.0}=8.6\\:\\rm m\/s"The vertical component of the initial speed
"v_y=v\\sin\\theta=8.6\\times \\sin 45^{\\circ}=6.1\\:\\rm m\/s"The maximum vertical height
"h=\\frac{v_y^2}{2g}=\\frac{6.1^2}{2\\times 9.8}=1.9\\:\\rm m" Answer: "1.9\\:\\rm m"
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