Projectile at an angle (sum of vectors)

[V0ODO0CH1LD]

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...

 

[mathman]

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.

 

[V0ODO0CH1LD]

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?

 

[mathman]

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.

 

[V0ODO0CH1LD]

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?

 

[mathman]

I am not sure what you are asking. However in general terms, any (2 dim.) vector can b resolved into horizontal and vertical components.

 

[azizlwl]

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