Question

A projectile is shot at an angle of `pi/4` and a velocity of `7 m/s`. How far away will the projectile land?

Answer 1

`x_"max"=4,99 " m"`

Explanation:

`v_i:"initial velocity"`
`t_"elapsed":"elapsed time for projectile"`
`v_x:"x component for initial velocity"`
`x_"max"=v_x*t_"elapsed"`
`v_x=v_i*cos alpha`
`t_"elapsed"=(2*v_i*sin alpha)/g`

`x_"max"=v_i*cos alpha*(2*v_i*sin alpha)/g`
`2*sin alpha*cos alpha=sin 2 alpha`
`alpha=pi/4" "2alpha=pi/2" "sin(pi/2)=1`
`x_"max"=(v_i^2*sin2 alpha)/g`

`x_"max"=(7^2 *1)/g`
`x_"max"=49/(9,81)`
`x_"max"=4,99 " m"`