Projectile at an angle (sum of vectors)

In summary: The force to get the body the additional 3.66 m/s comes from the initial input force of 10m/s. This is because the vertical and horizontal components are not added numerically, but instead calculated using the Pythagorean theorem. Therefore, the initial input force is still responsible for the total velocity of the object.In summary, when throwing something at a 30° angle with a velocity of 10m/s, the vertical component is 5m/s and the horizontal component is 5√3 m/s, which equals 8.66 approximately. The force to get the body the additional 3.66 m/s comes from the initial input force of 10m/s, as the vertical and
  • #1
V0ODO0CH1LD
278
0
If I throw something at a 30° angle with a velocity of 10m/s, the vertical component is 5m/s and the horizontal component is 5√3 m/s, which equals 8.66 approximately.

Where did the force to get the body those additional 3.66 m/s come from? I mean, I did only input a force to get the object to 10m/s...
 
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  • #2
The horizontal and vertical components aren't supposed to be added numerically. Use Pythagorean theorem to get the total, which is the 10 you started with.
 
  • #3
mathman said:
The horizontal and vertical components aren't supposed to be added numerically. Use Pythagorean theorem to get the total, which is the 10 you started with.

that means that throwing a 10kg projectile at a 45° angle with a velocity of 10m/s is equivalent to throwing the same projectile vertically with a velocity of 5√2 and then horizontally with a velocity of 5√2.

But I clearly have to input more force throwing something twice at (5√2)m/s then throwing that same something once at 10m/s.

How can those be equivalent?
 
  • #4
Doing it in two steps is different. Extreme example - start it horizontally at 100 m/sec, then reverse it with force to make it stop. You will have exerted lots of force, but the projectile will have stopped moving.
 
  • #5
mathman said:
Doing it in two steps is different. Extreme example - start it horizontally at 100 m/sec, then reverse it with force to make it stop. You will have exerted lots of force, but the projectile will have stopped moving.

So in the previous case: Is the sum of the horizontal and vertical vectors equal to the one at a 45° angle as long as we are only concerned with displacement and time?

Wouldn't it work if we were concerned with velocity or total distance traveled?
 
  • #6
I am not sure what you are asking. However in general terms, any (2 dim.) vector can b resolved into horizontal and vertical components.
 
  • #7
V0ODO0CH1LD said:
If I throw something at a 30° angle with a velocity of 10m/s, the vertical component is 5m/s and the horizontal component is 5√3 m/s, which equals 8.66 approximately.

Where did the force to get the body those additional 3.66 m/s come from? I mean, I did only input a force to get the object to 10m/s...

1. Its desirable to have the vertical and horizontal components of a velocity since in this case
the acceleration to gravity is acting downward. If no gravity involve or gravity in/opposite direction of the velocity then it is useless to resolve it into 2 components.

2. It is a VECTOR addition. Not a scalar addition. In scalar its NOT true 5+5√3 =10
But in Vector it is true, 5+5√3=10, a²+b²=c², 25+75=c² =>c=10
 
Last edited:

1. What is a projectile at an angle?

A projectile at an angle refers to an object that is launched or thrown at a specific angle with respect to the horizontal plane.

2. What is the sum of vectors in a projectile at an angle?

The sum of vectors in a projectile at an angle is the combination of the horizontal and vertical components of the object's velocity. This determines the total speed and direction of the projectile's motion.

3. How do you calculate the horizontal and vertical components of a projectile's velocity?

The horizontal component can be calculated using the formula Vx = V * cosθ, where V is the initial velocity and θ is the launch angle. The vertical component can be calculated using Vy = V * sinθ, where V is the initial velocity and θ is the launch angle.

4. What is the maximum height reached by a projectile at an angle?

The maximum height reached by a projectile at an angle is determined by the vertical component of its velocity. It is equal to Vy^2/2g, where Vy is the vertical component of the initial velocity and g is the acceleration due to gravity.

5. How does air resistance affect a projectile at an angle?

Air resistance can affect a projectile at an angle by slowing down its horizontal and vertical speed. This results in a shorter range and a lower maximum height reached by the projectile. However, the effect of air resistance is typically small for objects with a high initial velocity or a short flight time.

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