Answer:
[tex]v_0 =[/tex]1.71
Explanation:
the parabolic movment is described by the following equation:
[tex]y = tan(a)x-\frac{1}{2v_0^2(cos(a))^2}gx^2[/tex]
where y is the height of the ball, a is the angle of launch, [tex]v_0[/tex] the initial velocity, g the gravity and x is the horizontal distance of the ball.
So, if we want that the ball reach the hood, we will replace values on the equation as:
[tex]0.8 = tan(47)(5)-\frac{1}{2v_0^2(cos(47))^2}(9.8)(5)^2[/tex]
Finally, solving for [tex]v_0[/tex], we get:
[tex]v_0=\sqrt{\frac{-9.8(5)^2}{(0.8-tan(47)(5))2cos^2(47)}}[/tex]
[tex]v_0 =[/tex]1.71
