The problem involves a hovercraft's motion, specifically calculating its final velocity after a period of acceleration. The context is rooted in kinematics, focusing on vector components of velocity and acceleration.
There is ongoing exploration of the vector nature of velocity and acceleration, with some participants offering guidance on terminology and calculations. Multiple interpretations of angle adjustments are being considered, but no consensus has been reached on the final approach.
Participants note the importance of vector components and the distinction between speed and velocity. There is a suggestion to reconsider angles used in calculations, reflecting uncertainty about the setup.
aaronfue said:Homework Statement
A hovercraft is traveling 3m/s at 180 deg. The fan of the hovercraft causes a=4m/s2 at 50° for 10 seconds.
Homework Equations
What is the final velocity?
The Attempt at a Solution
v = 3cos180 - 4cos50*10?
gneill said:The velocity and acceleration should be vectors with both x and y components. Your attempt doesn't appear to deal with the y-component of the acceleration and its contribution to the final velocity (which will be a vector).
aaronfue said:So do I have to use the same equation with 4sin50° to get the velocity in the y direction, then I can take the magnitude of both vx & vy to get the final velocity?
Do I have to do the same for the velocity using 3sin180?
gneill said:Sure, sounds good.
A note on terminology: In general, "velocity" is a vector which has both speed and direction. The magnitude of a velocity vector is the speed. Speed is a scalar quantity with no particular associated direction.
That looks fine.aaronfue said:Ok. I calculated the velocity like so:
vx = 3cos180 + 4cos50*10 = 22.71 m/s
vy = 3sin180 + 4sin50*10 = 30.64 m/s
v = √22.712 + 30.642 = 38.14 m/s --> speed
No, the change in velocity will be in the same direction as the acceleration vector, but the final velocity will have its own angle (with respect to the x-axis). Work out the angle of the velocity vector from your calculated components of the velocity vector.I was thinking...should I use 130° instead of 50°, since the acceleration will be in the same direction as the velocity?