Introduction to vertical velocity
I’ve never seen a football player use his calculator to calculate the trajectory before kicking the game-winning field goal. I’ve never seen a football player whip out his calculator to calculate the path before kicking the game-winning field goal.
The bulk materials handling business is a better example. A designer will routinely use projectile motion to estimate the path of the outflow from heavy solids conveyor belts and bucket elevators.
Manufacturers utilize the anticipated trajectories to help construct material-gathering chutes and other structures.
The study of projectile motion serves as a useful opportunity to practice some parts of general problem solving while also learning new physics principles.
Understanding vectors and discovering that orthogonal vectors can be separated and treated independently (vertical and horizontal forces and motion can be treated separately and do not interact) are all made possible by studying projectile motion.
Definition
“The velocity away from or towards the earth’s centre is known as vertical velocity. The beginning velocity is Vyo, and the end velocity is Vy, both on the y-axis”.
A Vertical velocity is a specific form of velocity since it is constantly impacted by gravity’s acceleration in the vertical direction.
Any item hurled up, tossed down, or dropped in the vertical direction is impacted by this acceleration, which has a magnitude of around 10ms-2, directed downward, toward the centre of the earth.
The adage “what goes up must fall down” perfectly describes vertical velocity. The gravity of the earth causes items to fall back down to the earth at a rate of around 10ms-2.
SI Unit
The SI unit of vertical velocity is the same as that of tangential or linear velocity which is meter per second (ms-1). The velocity of a body is 1ms-1 if it covers a displacement of 1m in time 1s.
Formula
The general equation used to calculate the vertical velocity of an object is given as
Vy = Vy0 – gt
where Vy is the final vertical velocity, Vyo is the initial vertical velocity, g is gravitational acceleration and t is the time taken. The above formula can also be reformed for initial vertical velocity and time taken as
t = Vy – Vyo /g
Vyo = Vy + gt
Derivation
In order to derive the relation for vertical velocity, it is compulsory to study projectile motion first. The motion in which a body is thrown at a certain angle in such a way that it moves with constant horizontal velocity and at the same time it moves under the action of gravity is called projectile motion.
A football kicked by a player is the best example of projectile motion. The path followed by the projectile is called its trajectory which is parabolic in shape.
Let us consider that an object is thrown horizontally from a certain height with an initial velocity Vyo. After some time t, the object strikes the ground under the action of gravity g with final vertical velocity Vy. Now from the third equation of motion
Vf = Vi + at
Here the final velocity is Vy, the Initial velocity is Vyo and acceleration is g. Now by putting these values in the above equations we have
Vy = Vyo + gt
As we know that the gravitational acceleration in projectile motion is always negative so
Vy = Vyo – gt
The above relation shows the relation of vertical velocity with gravitational acceleration.
How to calculate the problems of Vertical velocity?
Example 1: With an initial vertical velocity of 10m/s, a helicopter drops a bench. Calculate the vertical velocity of the bench when it hits the ground in 4.5 seconds.
Solution: Manual method
Step 1: write given data values
Initial vertical velocity = vyo = 10m/s
Time = t = 4.5s
Gravitational acceleration = g 10m/s2
Vertical velocity = Vy =?
Step 2: Write general formula for net force
Vy = Vy0 – gt
Step 3: Put the given data values
Vy = Vy0 – gt
Vy = 10– (10)4.5s
Vy = 10– 45
Vy = -35m/s
Hence the vertical velocity of bench is -35m/s.
The above problem can also be solved using a vertical velocity calculator. It allows us to tackle issues quickly and effectively by leveraging vertical velocity.
It breaks down the problem into small bits, allowing pupils to spend more time understanding it. The problems can be handled by employing the strategies listed below.
Step 1: Choose the phrase you wish to compute from the drop-down menu.
Step 2: Place the given data values or required information into the calculator and press the calculate button.
As a consequence, the problem is figured out.
Example 2: For time
A golfer hits the ball with a 30 m/s starting vertical velocity. Calculate the time it takes the ball to hit the ground if the final vertical velocity is 20m/s.
Solution: Manual method
Step 1: write given data values
Initial vertical velocity = vyo = 30m/s
Time = t =?
Gravitational acceleration = g = 10m/s2
Vertical velocity = Vy =15m/s
Step 2: rewrite general formula for time
t = Vy – Vyo /g
Step 3: Put the given data values
t = 30- 15/10
t = 15/10
t = 1.5s
Hence the time taken is 1.5s.
Example 3: For initial vertical velocity
A cricket ball is hurled in the direction of the wickets. Calculate the first vertical velocity of the ball if it strikes the wickets after 2.5s with a velocity of 15m/s.
Solution: Manual method
Step 1: write given data values
Initial vertical velocity = vyo =?
Time = t = 2.5s
Gravitational acceleration = g =10m/s2
Vertical velocity = Vy =15m/s
Step 2: rewrite general formula for time
Vyo = Vy + gt
Step 3: Put the given data values
Vyo = 15+ (10)(2.5)
Vyo = 15+25
Vyo = 40m/s
Hence the initial vertical velocity is 40m/s.
Summary:
In mechanics, the vertical velocity is extremely important. It is hard to comprehend complicated physics topics involving two-dimensional motion without first grasping the concept of vertical velocity.
The concept of vertical velocity can be found in everything from kicking a football to launching missiles. When dealing with parabolic motions, you will undoubtedly need to analyze vertical velocity, which is a component of projectile motion.
Vertical velocity equations can be used to address any problem involving vertical motion. However, equations facilitate problem resolution, and calculators such as the vertical velocity calculator facilitate derivations.
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