Projectile Launch Angle Calculation with Given Launch Speed and Maximum Height

In summary, to find the launch angle of a projectile with a launch speed 6.4 times its speed at maximum height, you need to use the equation V0x^2 + V0y^2 = 6.4(V0x), solve for V0y, and then use the inverse tangent to find the launch angle. In this case, the launch angle was found to be 81.1 degrees.
  • #1
shell4987
43
0

Homework Statement


A projectile's launch speed is 6.4 times its speed at maximum height. Find the launch angle 0.


Homework Equations


I know that the x-axis has to be the horizontal and the y-axis, vertical. I know I also have to use the square root of V0x squared plus V0y squared = 6.4 (V0x) and that I need to solve for V0y and then the inverse tangent to find the launch angle.


The Attempt at a Solution


I tried letting V0x and V0y be the components of the initial velocity. Also, at max height, the speed of the projectile is V0x since it is traveling horizontally and that component of velocity is constant. I don't really know where to go from there because I don't know what to put for the V0x... I know how to figure out this problem, but I just don't know what V0x is or how to figure it out, does anyone have any clue on how to figure that out?
 
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  • #2
you're almost there...

square both sides... solve for Vx, in terms of Vy... then take Vy/Vx, then inverse tan.
 
  • #3
thank you SO much, i got the answer to be 81.1 degrees :)
 

FAQ: Projectile Launch Angle Calculation with Given Launch Speed and Maximum Height

What is the definition of projectile launch speed?

Projectile launch speed is the initial velocity at which a projectile is launched from a specific point, often measured in meters per second (m/s).

How is projectile launch speed calculated?

Projectile launch speed is calculated using the equation v = √(2gh), where v is the launch speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height from which the projectile is launched.

What factors affect projectile launch speed?

The factors that affect projectile launch speed include the angle of launch, the mass of the projectile, the air resistance, and the height from which the projectile is launched.

Can projectile launch speed be greater than the speed of light?

No, according to the theory of relativity, nothing can travel faster than the speed of light (299,792,458 m/s). Therefore, projectile launch speed cannot exceed this limit.

How does projectile launch speed affect the trajectory of a projectile?

The greater the projectile launch speed, the longer the projectile will travel and the higher it will go. This results in a flatter and longer trajectory. However, if the launch speed is too high, the projectile may overshoot the target or even go into orbit.

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