## Projectile at an angle (sum of vectors)

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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 Recognitions: Science Advisor 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.

 Quote by 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.
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?

Recognitions:

## Projectile at an angle (sum of vectors)

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.

 Quote by 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.
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?

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

 Quote by 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...
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

 Tags angle, vectors, velocity