Question Number 135558 by bemath last updated on 14/Mar/21
$$ \\ $$ A boy throws a ball at a vertical wall 4 m away. The ball is 2 m above ground when it leaves the girl's hand with initial velocity of 10√2 ��/�� at 45º. Horizontal component is reversed only. Where does the ball hit the ground after bounce?\\n
Commented bymr W last updated on 14/Mar/21
$${does}\:{the}\:{boy}\:{throw}\:{that}\:{ball}\:{in}\:{the} \\ $$ $${hand}\:{of}\:{the}\:{girl}? \\ $$
Answered by mr W last updated on 14/Mar/21
$${since}\:{the}\:{collision}\:{on}\:{the}\:{wall}\:{is} \\ $$ $${elastic}\:{and}\:{only}\:{the}\:{horizontal} \\ $$ $${component}\:{of}\:{ball}'{s}\:{velocity}\:{is} \\ $$ $${reversed},\:{we}\:{can}\:{treat}\:{as}\:{if}\:{the} \\ $$ $${wall}\:{is}\:{a}\:{mirror}. \\ $$ $${h}=−{u}\:\mathrm{sin}\:\theta\:{t}+\frac{\mathrm{1}}{\mathrm{2}}{gt}^{\mathrm{2}} \\ $$ $$\Rightarrow{t}=\frac{\mathrm{1}}{{g}}\left({u}\:\mathrm{sin}\:\theta+\sqrt{{u}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \:\theta+\mathrm{2}{gh}}\right) \\ $$ $${u}=\mathrm{10}\sqrt{\mathrm{2}}\:{m}/{s} \\ $$ $$\theta=\mathrm{45}° \\ $$ $${h}=\mathrm{2}\:{m} \\ $$ $${b}=\mathrm{4}\:{m} \\ $$ $${g}=\mathrm{10}\:{m}/{s}^{\mathrm{2}} \\ $$ $${u}\:\mathrm{sin}\:\theta={u}\:\mathrm{cos}\:\theta=\mathrm{10}\sqrt{\mathrm{2}}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}=\mathrm{10} \\ $$ $$\Rightarrow{t}=\frac{\mathrm{1}}{\mathrm{10}}\left(\mathrm{10}+\sqrt{\mathrm{10}^{\mathrm{2}} +\mathrm{2}×\mathrm{10}×\mathrm{2}}\right)=\mathrm{1}+\frac{\sqrt{\mathrm{35}}}{\mathrm{5}} \\ $$ $$\:\:\:\:\:\:\:\approx\mathrm{2}.\mathrm{18}\:{s} \\ $$ $${b}+{L}={u}\:\mathrm{cos}\:\theta\:{t} \\ $$ $${L}=\mathrm{10}×\left(\mathrm{1}+\frac{\sqrt{\mathrm{35}}}{\mathrm{5}}\right)−\mathrm{4}=\mathrm{6}+\mathrm{2}\sqrt{\mathrm{35}}\approx\mathrm{17}.\mathrm{83}\:{m} \\ $$ $${i}.{e}\:{the}\:{ball}\:{hits}\:{the}\:{ground}\:\mathrm{17}.\mathrm{83}{m} \\ $$ $${away}\:{from}\:{the}\:{wall},\:{or}\:\mathrm{13}.\mathrm{83}{m} \\ $$ $${behind}\:{the}\:{boy}. \\ $$
Commented bymr W last updated on 14/Mar/21
Commented bybemath last updated on 14/Mar/21
$${yes}...{sir}...{nice} \\ $$