# Finding the Velocity of a Projectile knowing only Launch Angle and Flight Time

• flyparnape
In summary: There are two launch parameters that determine the time in the air: the horizontal speed and the vertical speed.

#### flyparnape

Homework Statement
Quick question, how would I find the velocity of Projectile Motion without knowing the total distance
Relevant Equations
I'm given the object mass: 13.874g, Angle of Launch: 40˚, the horizontal length of 60cm and the time it lands on the ground: 4s. Also, gravity is obviously 9.8m/s
I don't know the distance or the horizontal velocity so I can't find any logical solution

The fact that the projectile was in the air for ##4s## must tell you something.

flyparnape said:
I don't know the distance
What does "horizontal length" mean?

Hint: Consider the vertical component of motion.

So horizontal length is the length of the object when placed at the angle of launch. Am I supposed to find the distance from the ground

flyparnape said:
So horizontal length is the length of the object when placed at the angle of launch. Am I supposed to find the distance from the ground
Where did the horizontal length come from? Is that mentioned in the problem statement?

PeroK said:
Where did the horizontal length come from? Is that mentioned in the problem statement?
The horizontal length comes from the position of the rocket before launch

flyparnape said:
The horizontal length comes from the position of the rocket before launch
Not sure how that is relevant. Could you please post the full problem statement so we can see what's being asked for in context?

flyparnape said:
The horizontal length comes from the position of the rocket before launch
Yes, the POSITION of the rocket, not the length of the rocket.

flyparnape said:
Also, gravity is obviously 9.8m/s^2

flyparnape said:
Homework Statement:: Quick question, how would I find the velocity of Projectile Motion without knowing the total distance
Relevant Equations:: I'm given the object mass: 13.874g, Angle of Launch: 40˚, the horizontal length of 60cm and the time it lands on the ground: 4s. Also, gravity is obviously 9.8m/s

I don't know the distance or the horizontal velocity so I can't find any logical solution
What aspect of the launch parameters determines the time in the air (for a flight that starts and finishes at the same height)?

horizontal length, and gravity

flyparnape said:
horizontal length, and gravity
I don't think that's the answer we were expecting. Normally, in projectile motion problems the horizontal length of an object is not relevant. In any case, the length of an object tells you nothing about launch speed and angle.

Please post the full problem statement. That way we'll know exactly what you're given and what you're asked to find.

flyparnape said:
So horizontal length is the length of the object when placed at the angle of launch.
I sense a language issue. By "horizontal length", do you mean how far the projectile moves horizontally between its launch and when it lands?

Here's is a picture of the object

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Interesting. Now (as previously advised) see if you can use the given information (that 4s, for instance) to figure out the vertical component of the initial velocity.

So, not actually a rocket. That takes care of one pointless mystery. Another two or three pages and we might actually figure out what the homework problem is.

Doc Al
If you are trying to determine the initial velocity of the projectile from the time of flight, then you should shoot it straight up in the air, i.e. make the "known angle" 90o.

flyparnape said:
horizontal length, and gravity
Neither of those are "launch parameters".
When you set up to launch an object on some trajectory, what aspects do you control?

If your objective is just to calculate the initial velocity, you have all the information you need. (And some that you don't!)

haruspex said:
Neither of those are "launch parameters".
When you set up to launch an object on some trajectory, what aspects do you control?
You control the angle of launch

flyparnape said:
You control the angle of launch
And the speed.
Or to look at it another way, the parameters are the horizontal speed and the vertical speed.
Of those four, is there just one that determines the time in the air, assuming the landing height is the same as the launch height?

## 1. How can I find the velocity of a projectile with only the launch angle and flight time?

The velocity of a projectile can be found using the formula v = g*tan(θ), where g is the acceleration due to gravity and θ is the launch angle. Flight time can be used to determine the value of g*tan(θ).

## 2. What if I don't know the value of g or the launch angle?

If you do not know the value of g or the launch angle, you will need to gather more information or use a different method to calculate the velocity. You can measure the distance traveled by the projectile and use the formula v = d/t, where d is the distance and t is the flight time. Alternatively, you can use a motion sensor to collect data on the projectile's motion and analyze it using mathematical equations.

## 3. Is it necessary to know the launch angle and flight time to find the velocity?

Yes, knowing the launch angle and flight time is necessary to calculate the velocity of a projectile. These two parameters are crucial in determining the trajectory of the projectile and its speed. Without this information, it would be impossible to accurately calculate the velocity.

## 4. Can I use this method to find the velocity of any projectile?

Yes, this method can be used to find the velocity of any projectile as long as you have the launch angle and flight time. However, the accuracy of the calculation may vary depending on external factors such as air resistance and wind.

## 5. What are some limitations of using this method to find the velocity of a projectile?

One limitation of using this method is that it assumes a constant acceleration due to gravity and neglects factors such as air resistance and wind, which can affect the velocity of the projectile. Additionally, this method may not be accurate for projectiles with very high velocities or for objects that do not follow a parabolic trajectory.