Projectile Motion: finding velocity if given range, angle, and height.

In summary, the conversation was about finding an equation for initial speed (V) given the initial angle, range, and initial height above ground. The formula provided by the speaker was incorrect and after starting from scratch, they were able to derive a new formula that takes into account gravitational acceleration. The final formula is v = √(0.5 * g * s2 / (cos2θ * (s * tanθ + h))).
  • #1
hmvince
44
0
Hey everyone!
I have been asked to find an equation with the subject of V (initial speed) with only the information given, angle above horizontal, range, and initial height above ground. I did attempt this myself and got the formula:
v = initial speed
θ = initial angle
s = range (total)
h = initial height above ground

v3(2s*tanθ) + v2(2h) + s2/cos2θ = 0

It is a cubic and so I left it in this form but I found this to be incorrect (will not show working as it is around a page) and have been over my work multiple times. Please help me with this!
 
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  • #2
Nevermind, with hard work and starting from scratch I managed to derive this formula!:

v = initial speed
θ = initial angle
s = range
h = height above ground (also works below)
g = gravitational acceleration (positive)let a = 0.5 * g * s2
let b = cos2θ * (s * tanθ + h)

v = Math.sqrt(a / b)

and it works!
thanks for all your hard work guys, it paid off this time
 

FAQ: Projectile Motion: finding velocity if given range, angle, and height.

What is projectile motion?

Projectile motion is the motion of an object through the air as a result of an initial velocity and the force of gravity. It follows a curved path known as a parabola.

How is velocity calculated in projectile motion?

In projectile motion, velocity is calculated by using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (9.8 m/s²), and t is the time elapsed.

How do you find the velocity of a projectile if given the range, angle, and height?

To find the velocity of a projectile, we can use the equation v = √(gR/2sinθ), where g is the gravitational acceleration, R is the range, and θ is the angle of projection. We can also use the equation v = √(2gh), where h is the height of the projectile.

Can the velocity of a projectile change during its flight?

Yes, the velocity of a projectile changes during its flight due to the acceleration of gravity. As the object moves higher, the velocity decreases, and as it moves lower, the velocity increases.

What factors affect the velocity of a projectile?

The velocity of a projectile is affected by the initial velocity, the angle of projection, the height of the projectile, and the air resistance. Other factors such as wind and air density can also affect the velocity of a projectile.

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