The horizontal range of the missile is b) 176 m
Explanation:
The motion of the missile is a projectile motion, so it consists of two independent motions:
- A uniform motion with constant velocity along the horizontal direction
- A uniformly accelerated motion with constant acceleration (equal to the acceleration of gravity) in the vertical-downward direction
To find the time of flight of the missile, we study the vertical motion. We can use the following suvat equation:
[tex]s=u_y t+\frac{1}{2}at^2[/tex]
where:
s = 75 m is the vertical displacement of the missile (the height of the building)
[tex]u_y=0[/tex] is the initial vertical velocity (the missile is thrown horizontally)
t is the time of flight
[tex]a=g=9.8 m/s^2[/tex] is the acceleration of gravity
Solving for t, we find the time of flight:
[tex]t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(75)}{9.8}}=3.91 s[/tex]
This means that the missile takes 3.91 s to reach the ground.
Now we study the horizontal motion: the missile moves with a constant horizontal velocity of
[tex]v_x = 45 m/s[/tex]
Therefore, the distance covered in a time t is
[tex]d=v_x t[/tex]
and by substituting t = 3.91 s, we find the horizontal range of the missile:
[tex]d=(45)(3.91)=176 m[/tex]
Learn more about projectile motion:
brainly.com/question/8751410
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