Instantaneous velocity of a object in projectile motion

[NightRunnerz]

Homework Statement

stone is thrown horizontally with a initial speed of 8.0 m/s (Vxi)
Air resistance is negligible. average acceleration due to gravity = 9.8 N/Kg (down) [ay]

Homework Equations

dx= Vxi/ time
Vfy= vyi + ay x time
Instantaneou velocity equation? :S

The Attempt at a Solution

okay so it tells me to find horizontal and vertical components of displacement and instantaneous velocity at time=0.0s/1.0s/2.0s and 3.0s isn't Vyi given (initial y velocity SINCE it's 0?) and (vxi is also give - 8.0 m/s)
BUt how do i find INSTANTANEOUS velocity?

 

[tiny-tim]

Welcome to PF!

Hi NightRunnerz! Welcome to PF!

… how do i find INSTANTANEOUS velocity?

Instantaneous velocity just means the velocity at that particular moment (ie, the word "instantaneous" is unnecessary )

(and if you need the speed, use Pythagoras! )

 

[NightRunnerz]

OKAY so by velocity you mean V as in speed right?
dotdotdot m/s2?
...m/s2?

 

[tiny-tim]

Hi NightRunnerz!

(just got up :zzz: …)

okay so it tells me to find horizontal and vertical components of displacement and instantaneous velocity at time …

OKAY so by velocity you mean V as in speed right?

No, speed and velocity are different.

Speed is the magnitude of velocity.

Velocity has components, speed doesn't.

The question tells you to find the horizontal and vertical components of instantaneous velocity … that's v_x and v_y.

dotdotdot m/s2?
...m/s2?

m/s² is acceleration

 

[rwisz]

I would approach this problem by first understanding the concept of instantaneous velocity. Instantaneous velocity refers to the velocity of an object at a specific moment in time, and it is calculated by taking the limit of the average velocity as the time interval approaches zero. In other words, it is the velocity at a single point in time.

In this case, the object is a stone thrown horizontally with an initial speed of 8.0 m/s and negligible air resistance. The average acceleration due to gravity is given as 9.8 N/Kg (down). To find the instantaneous velocity at different points in time, we can use the equation Vfy = vyi + ay x time, where Vfy is the final velocity, vyi is the initial velocity, ay is the acceleration due to gravity, and time is the elapsed time.

At time t=0.0s, the stone has just been thrown and is at its initial position. Therefore, its initial velocity in the y-direction (Vyi) is 0 m/s, as there is no initial vertical velocity. Plugging this into the equation, we get Vfy = 0 + (9.8 m/s^2)(0.0 s) = 0 m/s. This means that at t=0.0s, the instantaneous velocity of the stone is 0 m/s in the y-direction.

At time t=1.0s, the stone has been in motion for 1 second. Using the same equation, we get Vfy = 0 + (9.8 m/s^2)(1.0 s) = 9.8 m/s. This means that at t=1.0s, the instantaneous velocity of the stone in the y-direction is 9.8 m/s.

Similarly, at t=2.0s and t=3.0s, we can calculate the instantaneous velocity in the y-direction as 19.6 m/s and 29.4 m/s, respectively.

To find the instantaneous velocity in the x-direction, we can use the equation dx = Vxi x time, where dx is the displacement in the x-direction and Vxi is the initial velocity in the x-direction. In this case, the initial velocity in the x-direction is given as 8.0 m/s. Therefore, at t=0.0s, the instantaneous velocity in the x-direction is also 8.0 m/s