Finding magnitude and direction of a rocket

AI Thread Summary
To find the magnitude and direction of a rocket fired at an initial velocity of 50 m/s at a 35-degree angle, the horizontal and vertical components of velocity were calculated. The magnitude of the velocity at t=4s was determined to be 42.289 m/s. Displacement in the x-direction was found to be 163.83 m, while the y-displacement was 36.32 m. To find the direction, the correct approach is to use the inverse tangent of the vertical displacement over the horizontal displacement. This method clarifies that the angle is derived from the velocity components, not the displacements.
CandyApples
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Homework Statement


A model rocket has been fired with V0=50m/s at 35 degrees above horizontal. Find magnitude and direction at t=4s.


Homework Equations


V = V0+at, displacement = v0t + .5at2


The Attempt at a Solution


I have successfully found the magnitude by setting Vx= 50*cos35 and Vy = 50sin35 -4g then taking the square root of each direction squared to find the magnitude is equal to 42.289 m/s. I am having trouble now, figuring out what to do to figure out the direction. I have calculated displacement of x to be 163.83m and displacement of y to be 36.32m by using the displacement equation. Any hints on how to find the angle? I thought inverse tangent of y/x would give me the correct displacement, however it did not.
 
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Be careful. "Find the magnitude and direction" is ambiguous, but based on the fact you got the correct answer for the magnitude by taking the magnitude of the velocity, I assume the question is "Find the magnitude and direction of the velocity", not "Find the magnitude of the velocity and the direction of the displacement", which is what you solved.
 
If you draw a triangle you will see that Vx and Vy form a right triangle with V. You can use trig(tan) to find the angle.
 

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