1) The landing spot of the projectile is given by
2) The common variable is the time
Explanation:
1)
The motion of a projectile consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction
The landing spot can be determined in the following way:
- First of all, we analyze the vertical motion to find the time of flight of the projectile. This can be done by using the suvat equation
where
h is the vertical displacement of the projectile, which corresponds to the height from which the projectile has been fired, above the ground
u = 0 is the initial vertical velocity
is the acceleration of gravity
t is the time of flight
Solving for t,
- After finding the time of flight, we analyze the horizontal motion, which is a uniform motion with constant horizontal velocity . Therefore, the horizontal distance covered is given by
And substituting the time of flight,
2)
Since the horizontal motion is uniform, the horizontal component of the displacement of the projectile is given by
where is the horizontal velocity and t is the time.
The vertical motion is accelerated, so the vertical component of the displacement is given by
where g is the acceleration of gravity and t is the time.
Therefore, from the two equations we see that the common variable is t, the time.
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