Motion of a body thrown in horizontal direction


In motion of a body thrown in horizontal direction, which of these is true about the components of velocity of the system? (Assume system is a ground projectile.)

a. Only vertical component is constant
b. Only horizontal component is constant
c. Both horizontal and vertical components are constant
d. None of the components is constant

Answer) b.

Motion of a body thrown in horizontal direction : a combination of horizontal motion with constant horizontal velocity and vertical motion with a constant downward acceleration due to gravity.

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Projectile motion is free fall with an initial horizontal velocity
To understand the motion a projectile undergoes, first examine Fig 01. The red ball was dropped at the same instant the yellow ball was launched horizontally.

Fig. 01 This is a strobe photograph of two table-tennis balls released at the same time. Even though the yellow ball is given an initial horizontal velocity and the red ball is simply dropped, both balls fall at the same rate.

The curved path shown in Fig 01. is the combination of constant horizontal motion and vertical motion that undergoes acceleration due to gravity.

If air resistance is disregarded, both balls hit the ground at the same time. By examining each ball’s position in relation to the horizontal lines and to one another, we see that the two balls fall at the same rate. This may seem impossible because one is given an initial velocity and the other begins from rest. But if the motion is analyzed one component at a time, it makes sense.

First, consider the red ball that falls straight down. It has no motion in the horizontal direction. In the vertical direction, it starts from rest ($\ v_{0y}$ = 0 m/s) and proceeds in free fall. Thus, the kinematic equations from the chapter “Motion in One Dimension” can be applied to analyze the vertical motion of the falling ball, as shown on the next page. Note that on Earth’s surface the acceleration ($\ a_y$) will equal $\ g$ ($\ 9.8 m/s^2$) because the only vertical component of acceleration is free-fall acceleration. 

$\ a_y = g$
$\ v_y = gt$
$\ y = \frac{1}{2}gt^2$

Now consider the components of motion of the yellow ball that is launched in Fig 01. This ball undergoes the same horizontal displacement during each time interval. This means that the ball’s horizontal velocity remains constant (if air resistance is assumed to be negligible). Thus, when the kinematic equations are used to analyze the horizontal motion of a projectile, the initial horizontal velocity is equal to the horizontal velocity throughout the projectile’s flight. A projectile’s horizontal motion is described by the following equation.

$\ v_x = v_{0} =constant$
$\ x = v_{0}t $

Next consider the initial motion of the launched yellow ball in Fig 01. Despite having an initial horizontal velocity, the launched ball has no initial velocity in the vertical direction. Just like the red ball that falls straight down, the launched yellow ball is in free fall. The vertical motion of the launched yellow ball is described by the same free-fall equations. In any time interval, the launched ball undergoes the same vertical displacement as the ball that falls straight down. For this reason, both balls reach the ground at the same time.

To find the velocity of a projectile at any point during its flight, find the vector that has the known components. Specifically, use the Pythagorean theorem to find the magnitude of the velocity, and use the tangent function to find the direction of the velocity.

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