Question #2b130

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Answer 1 · 2017-02-05T15:55:41

$h_("max")" is 50 meters"$
$"time traveled is 6.38 seconds"$

$"The maximum x value can be calculated using formula:"$

$x_("max")=(v_i^2*sin 2alpha)/g$

$"where " x_("max")=100" "m" , "v_i="initial velocity"$
$alpha=45$
$2 alpha=2*45=90$
$sin 90=1$

$100=(v_i^2*sin 90)/(2*g)$

$100=v_i^2/(2.g)$

$2.g=v_i^2/100$

$"maximum height :"h_("max")=(v_i^2*sin^2 alpha)/(2g)$

$h_("max")=(v_i^2*sin^2 alpha)/(v_i^2/100)$

$h_("max")=cancel(v_i^2)*sin^2 alpha*100/cancel(v_i^2)$

$h_("max")=100*((sqrt 2)/2)^2=100*2/4=50 " m"$

$"we can write "h_("max")=1/2*g*t^2$

$50=1/2*9.81*t^2$

$100=9.81*t^2$

$t^2=100/(9.81)$

$t^2=10.19368$

$t=3.19 " s"$

$"time traveled"=2*3.19=6.38" "s$