Answer:
The value is [tex]x = 11.81 \ m[/tex]
Explanation:
From the question we are told that
The height is h = 2.0 m
The height of the window is [tex]d = 9.0 \ m[/tex]
The initial velocity of the rock is [tex]u = 20 \ m/s[/tex]
The angle at which it is thrown is [tex]\theta = 40[/tex]
Generally the vertical component of the velocity of the stone is mathematically represented as
[tex]v_y = 20 sin (40)[/tex]
=>[tex]v_y = 12.86 \ m/s[/tex]
Generally the height of the window from the ground is mathematically represented as using kinematic equation as
[tex]d = h + v_yt + \frac{1}{2} gt^2[/tex]
=> [tex]9 = 2 +12.86 t + \frac{1}{2} * - 9.8 t^2[/tex]
Here g is negative -9.8 m/s^2 because the direction of the stone is against gravity
So
[tex]4.9 t^2 -12.86 t + 7 =0[/tex]
Solving this quadratic equation using quadratic formula we obtain
t = 0.770 s
Generally the velocity of the stone on the x axis is mathematically represented as
[tex]v_x = 20 * cos(40 )[/tex]
=> [tex]v_x = 15.32 \ m/s[/tex]
Generally the distance between the person throwing the rock and the window is mathematically represented as
[tex]x = v_x * t[/tex]
=> [tex]x = 15.32 * 0.771[/tex]
=> [tex]x = 11.81 \ m[/tex]
