Determining range without the angle

[StarryNights]

One problem I just did asked me for the minimum amount of info needed for determining the range of an object according to projectile motion. I chose initial velocity, angle, and value of gravity. The correct answer is initial velocity and value of gravity. The solution says that once we know the initial velocity then we can break it up into its x and y components and then find the range. How would you determine the x and y components of the initial velocity vector without the angle? Thanks!

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[Northwesterly]

Velocity measures both speed and direction. (If the question asked about speed rather than velocity, you would need speed, gravity, and angle.)

 

[StarryNights]

Velocity measures both speed and direction. (If the question asked about speed rather than velocity, you would need speed, gravity, and angle.)

Yea, but let's say you're given initial velocity as 10 m/s northwest. But first you need to break it into the vertical component to find the time it hits the ground. Then you can multiply the time by the horizontal velocity component to find the range. How are you supposed to get the vertical component of 10 m/s northwest without the angle?

 

[PiBond]

Yea, but let's say you're given initial velocity as 10 m/s northwest. But first you need to break it into the vertical component to find the time it hits the ground. Then you can multiply the time by the horizontal velocity component to find the range. How are you supposed to get the vertical component of 10 m/s northwest without the angle?

Northwest would be a 45 degree angle

 

[StarryNights]

Northwest would be a 45 degree angle

Lol, I sort of threw NW out there as an example, but it would still be NW if the angle was 43 or 72 or 25 right? Granted 25 would be referred to as 25 north of west, but it's still NW. So without an exact angle, I don't see how you'd find the exact vertical component. But thanks for helping nonetheless . I'm going to ask my Kaplan teacher as this question is so ambiguous.

Actually, I think my angle examples refer to NE, but the idea is similar regardless.

 

[TieuBachHo]

Edit Note: This is totally wrong but can't delete! :<

hello there,
You actually don't need to know the angle to calulate the volocity components. With the given information, you can find out the height by using the conservation of energy mgh (final) = 1/2mv^2 (initial). Note: at the maximum height the final velocity is zero. Once you get the vertical height, you can use 0 = v(final)^2 = v(initial)^2 + 2gh. (+/- sign should depend on how you chose the direction of motion and I am just writing conventional formula) Note: this is in the y-direction and v(initial)^2 is the initial velocity in the Y-direction. From here you can solve your problem. Just make sure you consult it back with your proctor/instructor if he/she has any other approach.

 

[StarryNights]

hello there,
You actually don't need to know the angle to calulate the volocity components. With the given information, you can find out the height by using the conservation of energy mgh (final) = 1/2mv^2 (initial). Note: at the maximum height the final velocity is zero. Once you get the vertical height, you can use 0 = v(final)^2 = v(initial)^2 + 2gh. (+/- sign should depend on how you chose the direction of motion and I am just writing conventional formula) Note: this is in the y-direction and v(initial)^2 is the initial velocity in the Y-direction. From here you can solve your problem. Just make sure you consult it back with your proctor/instructor if he/she has any other approach.

That's an interesting approach and I'll look it over a bit more in depth. At the moment though, I don't think it works. With conservation of energy that you listed above mgh = (1/2) mv^2 without taking direction into account, you're assuming that all of the initial kinetic energy is converted to potential energy at the max height. This wouldn't be the case because at the max height, the horizontal velocity component is still present since it stays constant throughout the flight (so not all of the kinetic energy is converted to potential). It would work if you used only the initial vertical velocity, but as I was wondering above, how would you get the initial vertical velocity without the angle?

Thanks for your help either way, and I will apply this to an actual problem to make sure.

 

[TieuBachHo]

You are right ... I am suck at projectile motion More review for me then. Actually now I am thinking 'bout it ... you can shoot an object at diff. angles with the same initial speed will give you diff. horizontal ranges. I am inclined to think that this is a misinterpretation somehow. Good luck though and don't forget to post it up if you can find a solution.

 

[Isoprop]

Lol, I sort of threw NW out there as an example, but it would still be NW if the angle was 43 or 72 or 25 right? Granted 25 would be referred to as 25 north of west, but it's still NW. So without an exact angle, I don't see how you'd find the exact vertical component. But thanks for helping nonetheless . I'm going to ask my Kaplan teacher as this question is so ambiguous.

Actually, I think my angle examples refer to NE, but the idea is similar regardless.

The idea of a vector is that you know the direction. So you know the angle or can figure it out.

 

[StarryNights]

The idea of a vector is that you know the direction. So you know the angle or can figure it out.

I think this is the case like others have stated, and I'm making it more complicated than it needs to be. I'm not very good with qualitative questions, horrible actually. I approached this question by thinking through how I'd solve it with numbers and was irked when they didn't give me the angle. Oh well...

 

[Econ2MD]

Velocity is a vector quantity = speed and direction (or angle, if you prefer).

Speed is a scalar quantity = just speed, no direction.

Geometry can give you the component parts. The y component and gravity allow you to solve for time of flight. The x component and time will give you the distance traveled in the x direction.

Your logic is right, just a definition thing. Maybe review which quantities are scalar and which are vector.