Question

Question #2b130

Answer 1

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

Explanation:

`"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`