Question Number 16155 by Tinkutara last updated on 18/Jun/17
$$\mathrm{A}\:\mathrm{body}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{m}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{speed}\:{v}\:\mathrm{making}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{vertical}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{change}\:\mathrm{in} \\ $$$$\mathrm{momentum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{along}\:\mathrm{the}\:\mathrm{Y}- \\ $$$$\mathrm{axis};\:\mathrm{between}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{point}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{highest}\:\mathrm{point}\:\mathrm{of}\:\mathrm{its}\:\mathrm{path}? \\ $$
Answered by ajfour last updated on 18/Jun/17
$${y}\:{component}\:{of}\:\:{initial} \\ $$$$\:\:\:\:\:\:\:\:{momentum}\:=\boldsymbol{{mv}}\mathrm{cos}\:\boldsymbol{\theta} \\ $$$$\:{y}\:{component}\:{at}\:{of}\:{momentum} \\ $$$$\:{when}\:{at}\:{highest}\:{point}\:{of}\:{its} \\ $$$$\:\:\:\:\:\:\:\:{path}\:=\:\mathrm{0} \\ $$$$\:\boldsymbol{{change}}\:\boldsymbol{{in}}\:\boldsymbol{{y}}-{component} \\ $$$$\:{of}\:\boldsymbol{{momentum}}\:=\:−\boldsymbol{{mv}}\mathrm{cos}\:\boldsymbol{\theta}\:. \\ $$
Commented by Tinkutara last updated on 19/Jun/17
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$