1) The horizontal range of the bullet is 884 m
2) The maximum height attained by the bullet is 383 m
Explanation:
1)
The motion of the bullet is a projectile motion, which consists of two separate motions:
- A uniform motion (constant velocity) along the horizontal direction
- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction
From the equation of motions along the x- and y- directions, it is possible to find an expression for the horizontal range covered by a projectile, and it is:
where
u is the initial speed of the projectile
is the angle of projection
is the acceleration of gravity
For the bullet in the problem, we have
u = 100 m/s (initial speed)
(angle)
Solving the equation, we find the horizontal range:
2)
To find the maximum height, we have to analyze the vertical motion of the bullet. We can do it by using the following suvat equation:
where
is the vertical velocity of the bullet after having covered a vertical displacement of
is the initial vertical velocity
is the acceleration (negative, since it points downward)
The vertical component of the initial velocity is given by
Also, the maximum height s is reached when the vertical velocity becomes zero,
Substituting into the equation and re-arranging for s, we find the maximum height:
Learn more about projectile motion:
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