Finding the velocity with out time (s)

In summary, to find the velocity of the projectile as it leaves the launcher, you need to use the given information of the table/launcher height and the distance the projectile landed. By setting up a vertical and horizontal line on the x-y coordinates system, you can determine the position of the projectile and use equations to solve for the initial velocity. Remember that the initial velocity in the vertical component is 0.
  • #1
alniquette
1
0

Homework Statement


A launcher is on top of a table and fire the projectile horizontally. The table/launcher height is 1.1 m and the projectile landed 3.2 m away from the table.
h=1.1 m
R=3.2 m

Find the velocity of the projectile as it leaves the launcher.

Homework Equations


tanθ=y/x
Δx = V(i)t + 1/2at^2


The Attempt at a Solution



θ = tan^-1(1.1/3.2) θ= 18.97°
After this I am lost. I assume I need the angle but I'm not sure for what.

I think I may need to solve for both x and y. My x and y values are (0,1.1) (3.2,0)

x = V(i)t ?
y = h -1/2gt^2 ?

Since I don't have t I don't what other equations I can use.

Please let me know if I am on the right track!
Thank you.
 
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  • #2
On the x-y coordinates system, make a vertical and a horizontal lines.
The vertical line starts from zero and moves according to velocity.
The horizontal line moves from zero according to velocity and acceleration too.
The intersection of these lines determine the position of the projectile.
Remember it is only one projectile.
 
  • #3
From the equation y(t)=0 you obtain the time needed by the projectile to land, call this time for example [itex]t_\ell[/itex]. Then because [itex]x(t_\ell)=R[/itex] then from the equation

[itex]R=V(i)t_\ell[/itex]

you can find V(i).
 
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  • #4
Hint: Read the question and look what it given.
 
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  • #5
And if the projectile was fired horizontally, the initial velocity in the vertical component is 0. So, look at all your kinematic equations, solve for t and then solve for initial velocity in horizontal component.
 
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What is velocity?

Velocity is a measure of the rate at which an object changes its position. It is a vector quantity, meaning it has both magnitude (speed) and direction.

How is velocity calculated?

Velocity can be calculated by dividing the change in an object's position by the amount of time it takes for that change to occur. This is represented by the equation v = ∆x/∆t, where v is velocity, ∆x is change in position, and ∆t is change in time.

Why is time not needed to calculate velocity?

Time is not needed to calculate velocity if the initial and final positions of an object are known. This is because velocity is a measure of how much an object's position changes, not how long it takes for that change to occur.

What units is velocity measured in?

Velocity is typically measured in meters per second (m/s) in the metric system, or feet per second (ft/s) in the imperial system. It can also be measured in other units such as kilometers per hour (km/h) or miles per hour (mph).

How is velocity different from speed?

Velocity and speed are often used interchangeably, but they are actually different concepts. While speed is a measure of how fast an object is moving, velocity also takes into account the direction of the movement. This means that two objects can have the same speed but different velocities if they are moving in different directions.

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