Projectile motion refers to the motion of an object that is launched into the air and moves along a curved path under the influence of gravity. In this scenario, a body is projected horizontally from a height of 78.4m with an initial velocity of 10 m/s.



When a body is projected horizontally, its initial velocity in the vertical direction is zero. However, in the horizontal direction, the initial velocity remains constant. Here, the initial velocity is given as 10 m/s.

The time after which we need to determine the body's velocity is 3 seconds.



In projectile motion, the vertical and horizontal motions are independent of each other. The vertical motion is influenced by gravity, causing the body to accelerate downwards at a rate of 10 m/s².

Using the equation of motion, h = ut + (1/2)gt², where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time, we can calculate the height at any given time.

Given that the initial height is 78.4m and the time is 3 seconds, we can substitute these values into the equation:

h = (0) + (1/2)(10)(3)²
h = 0 + (1/2)(10)(9)
h = 0 + 45
h = 45m

Therefore, after 3 seconds, the body has descended 45 meters vertically.



Since the body is projected horizontally, there is no acceleration in the horizontal direction. Therefore, the horizontal velocity remains constant throughout the motion.

The horizontal displacement can be calculated using the equation d = vt, where d is the displacement, v is the velocity, and t is the time.

Given that the initial velocity is 10 m/s and the time is 3 seconds, we can substitute these values into the equation:

d = (10)(3)
d = 30m

Therefore, after 3 seconds, the body has traveled a horizontal distance of 30 meters.



To determine the final velocity, we need to find the magnitude of the resultant velocity, which is the vector sum of the horizontal and vertical velocities.

The horizontal velocity remains constant at 10 m/s, and the vertical velocity can be calculated using the equation v = u + gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time.

Given that the initial vertical velocity is 0 m/s and the time is 3 seconds, we can substitute these values into the equation:

v = (0) + (10)(3)
v = 30 m/s

Therefore, after 3 seconds, the body has a final velocity of 30 m/s, which is the magnitude of the resultant velocity.



In summary, when a body is projected horizontally from a height of 78.4m with an initial velocity of 10 m/s, its vertical motion is influenced by gravity, causing it to descend 45 meters after 3 seconds. The horizontal motion

31.6 m/s