Finding Launch Angle Using Projectile Motion Equations

In summary, the speed of a projectile is 3/4 of its initial speed and it goes half way up before having its velocity calculated.
  • #1
Imuell1
10
0

Homework Statement



at 1/2 of its maximum height, the speed of a projectile is 3/4 of its initial speed. what was its launch angle?(ignore any effects due to air resistance.)

Homework Equations


The Attempt at a Solution



I don't even know where to begin.
 
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  • #2
did you try looking at the projectile motion equations and seeing how you can work with them knowing that you can put your velocity at half of its max height in terms of the initial velocity?
 
  • #3
no i didn't try that. i am still so confused. which equation would i start with?
 
  • #4
This problem is a little tricky, but not too much so, if you focus on velocity and speed.

Keep in mind what speed is at all points. It is the |velocity|.

At any point |V| = (Vx2 + Vy2)1/2

Then all you have to do is figure the velocity in the vertical direction when it is gone half way and compare the |velocities| (speed) according to what the problem asks.
 
  • #5
Ugh, I am still so confused. I emailed my professor also and he said to use the equation Vy^2-Vyo^2=2ay and to put H in terms of Vy. For some reason I still have no idea where to begin still. I got y=(Vy^2-Vyo^2)/2a but even if that is correct, I don't know what to do next.
 
  • #6
By all means that is the correct equation to use. At the H/2 point how fast is Vy?

Isn't it

Vh/22 = Vo2 -2*g*H/2 ?

And you know that at H (which is max height)

Vh2 = 0 = Vo2 -2*g*H

So ... substituting in the first one you get

Vh/22 = 2*g*h -2*g*H/2 = 2*g*H/2 = (Vo2)/2

That is a very important result.

Now look at my initial hint ...
 
  • #7
when y=h, H=-Vyo^2/2a

so then to find the velocity of h/2 do i make the equation
H/2=(Vy^2-Vyo^2)/2a ?

then i substitute for H and get
(-Vyo^2/2a)/2=(Vy^2-Vyo^2)/2a?
 
  • #8
Imuell1 said:
when y=h, H=-Vyo^2/2a

so then to find the velocity of h/2 do i make the equation
H/2=(Vy^2-Vyo^2)/2a ?

then i substitute for H and get
(-Vyo^2/2a)/2=(Vy^2-Vyo^2)/2a?

What I did was take the additional fact that |Vh/2| = 3/4 |Vo|

Take advantage of the fact that Vx is constant through out.

Since Vh/22 = Vx2 + Vyh/22 = (3/4*Vo2)

Just expand using the knowledge that at H/2 Vy2 = 2*Vyh/22
 

1. What is the "launch angle" in science?

The launch angle, also known as the initial angle, is the angle at which an object is launched or projected into the air. In science, it is often used to describe the angle at which a projectile, such as a ball or a rocket, is launched from a horizontal surface.

2. How is the launch angle calculated?

The launch angle is typically calculated using trigonometry. It is the angle between the horizontal line and the line connecting the launch point and the highest point of the trajectory. This angle can be determined using the formula: θ = tan-1(vy/vx), where θ is the launch angle, vy is the initial vertical velocity, and vx is the initial horizontal velocity.

3. What factors affect the launch angle of a projectile?

The launch angle of a projectile can be affected by several factors, including the initial velocity, the gravitational force, and air resistance. The shape and size of the object, as well as the surface it is launched from, can also impact the launch angle.

4. Why is the launch angle important in science?

The launch angle is important in science because it helps us understand and predict the trajectory of a projectile. By knowing the launch angle and other factors, we can determine the maximum height, range, and time of flight of the object. This is crucial in fields such as engineering, physics, and sports.

5. How can the launch angle be adjusted?

The launch angle can be adjusted by changing the initial velocity, adjusting the angle of the launching surface, or using external forces such as a ramp or a slingshot. In some cases, the shape and weight distribution of the projectile can also be altered to change the launch angle.

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