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3. Someone at the third-floor window (12.0 m above the ground) hurls a ball downward at an angle of
45 degrees with a speed of 25 m/s. How fast will the ball be traveling when it strikes the sidewalk
below?​

Answer :

Answer:

[tex]v=29.3283\ m.s^{-1}[/tex]

Explanation:

Given:

  • height of point from where the ball is projected, [tex]h=12\ m[/tex]
  • angle of projection of the ball below the horizontal, [tex]\theta=45^{\circ}[/tex]
  • initial velocity of projection, [tex]u=25\ m.s^{-1}[/tex]

Now we find the vertical component of the initial velocity downwards:

[tex]u_y=u.\sin\theta[/tex]

[tex]u_y=25\times \cos45^{\circ}[/tex]

[tex]u_y=17.6777\ m.s^{-1}[/tex]

Now the final vertical velocity of the ball when it hits the ground:

using the equation of motion,

[tex]v_y^2=u_y^2+2.g.h[/tex]

[tex]v_y^2=17.6777^2+2\times 9.8\times 12[/tex]

[tex]v_y=23.402\ m.s^{-1}[/tex]

Since the horizontal component of the motion is uniform since no force acts in the horizontal direction:

[tex]v_x=u_x=25\cos45[/tex]

[tex]v_x=17.6777\ m.s^{-1}[/tex]

Now the resultant final velocity:

[tex]v=\sqrt{(17.6777)^2+(23.402)^2}[/tex]

[tex]v=29.3283\ m.s^{-1}[/tex]

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