Answer:
- horizontal component of the velocity: [tex]v_h[/tex] (because it is constant)
- vertical component of the velocity: 0
- vertical component of the acceleration: [tex]-g=-9.8 m/s^2[/tex] (downward)
Explanation:
The motion of a projectile consists of two independent motions:
- Along the horizontal direction, there are no forces acting on the projectile (if we neglect air resistance), therefore the horizontal acceleration is zero and the horizontal component of the velocity, vh, is constant
- Along the vertical direction, there is only one force acting on the projectile: the force of gravity, downward, which produces a constant downward acceleration of [tex]g=9.8 m/s^2[/tex]. As a consequence, the vertical component of the velocity changes according to
[tex]v_v(t) = v_v-gt[/tex]
where vv is the initial vertical velocity and t the time. According to this equation, the vertical component of the velocity decreases first, then becomes zero at the point of maximum height, then becomes negative (= changes direction and points downward)
So, in summary, at the highest point of the trajectory we have:
- horizontal component of the velocity: [tex]v_h[/tex] (because it is constant)
- vertical component of the velocity: 0
- vertical component of the acceleration: [tex]-g=-9.8 m/s^2[/tex] (downward)
At the highest point, the final vertical velocity is zero, and the final horizontal velocity is equal to the initial horizontal velocity.
The acceleration due to gravity acting on the object is always directed downwards.
In a projectile motion, the velocity of projected upwards decreases as the object moves upwards and eventually become zero at the maximum height.
The velocity of an object projected upwards is given as;
[tex]v_y = v_0 -gt[/tex]
At the highest point, the final vertical velocity is given as;
[tex]v_y_f= 0[/tex]
The horizontal velocity is always constant because it is not affected by gravity.
At the highest point, the final horizontal velocity is given as;
[tex]v_x_f = v_x_0[/tex]
The acceleration due to gravity acting on the object is always directed downwards.
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