How to solve a projectile sort problem with given linear and angular velocity?

[newemily]

how to solve a problem in which linear velocity and angular velocity (in the same direction) are given at the same time in a projectile motion .. how to calculated all the related values like the distance covered .. and consequently what is happening after that ... like ... m=160g diameter=.07m angular velocity=-10j rev/s and u=-25j m/s

 

[Doc Al]

I'm not clear on the problem setup. Please state the complete problem exactly as given.

 

[Moetasim]

To solve this projectile sort problem, we can use the equations of motion for projectile motion. First, we need to identify the given values and assign them to their respective variables. In this case, the given linear velocity u is -25j m/s, and the given angular velocity ω is -10j rev/s. The mass of the projectile is 160g, which can be converted to 0.160kg, and the diameter is 0.07m.

Next, we can use the equation v = u + at to find the final velocity of the projectile. Since we know the initial velocity (u), acceleration (a), and time (t = 1 rev/ω), we can plug in the values and solve for v.

v = -25j m/s + (-10j rev/s)(1 rev/-10j rev/s)
v = -25j m/s - 1 rev/s
v = -24j m/s

Now, we can use the equation s = ut + 1/2at^2 to find the distance covered by the projectile. Again, since we know the initial velocity, acceleration, and time, we can plug in the values and solve for s.

s = (-25j m/s)(1 rev/-10j rev/s) + 1/2(-10j rev/s)(1 rev/-10j rev/s)^2
s = -2.5j m + 0.05j m
s = -2.45j m

We can also use the equation ω = ω0 + αt to find the angular velocity after 1 rev. Since ω0 (initial angular velocity) is given as -10j rev/s and α (angular acceleration) is 0, we can simply plug in the values and solve for ω.

ω = -10j rev/s + 0(1 rev/-10j rev/s)
ω = -10j rev/s

From this, we can see that the angular velocity remains constant at -10j rev/s after 1 rev, while the linear velocity decreases from -25j m/s to -24j m/s and the projectile covers a distance of -2.45j m. We can also calculate the final position of the projectile by using the equation x = x0 + vt, where x0 is the initial position (which we can assume to be 0 since it is not given).

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