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bolini
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Can anyone help me with the terminal velocity of a lacrosse ball?
Approximations would help too.
Thanks.
Approximations would help too.
Thanks.
bolini said:Not sure how to include resistance in the equation because it varies depending on the velocity which is changing until 33m/s is achieved.
Actually, an object never reaches terminal velocity, it only approaches it. The solution to the time and distance it takes to 'approach' terminal velocity (say reach .99V_t) involves a non linear differential equation (mg - cpAv^2 = mdv/dt), the solution of which is beyond me at this point, but it involves a natural log term I think and probably 'e' raised to some power. But on a practical level, terminal velocity is ordinarily reached (approached) in less than 9 seconds (but much less for lighter objects like a feather or penny). So you are correct in that it would take a height much greater than 180 feet for the ball to attain a speed of 33m/s or so when you consider air resistance. I'm guessing that it might be around 500 feet or so.bolini said:I'm attempting to help my son with a elementary school project that measures the impact crater of a ball at different heights. I thought it would be cool to see if we could achieve terminal velocity, but at 180 feet without considering air resistance, I think we are already too high to practically consider.
I believe the first equation basically used air resistance as the square of velocity. I am curious now, even though we probably won't look for a building or bridge high enough, what the height actually would be. If you could help me incorporate air resistance into the kinematic equation I used, that would be helpful.
Thanks for your help up until this point. I forgot how interesting physics used to be for me.
Terminal velocity is the maximum speed that an object can reach when falling through a fluid, such as air or water. It occurs when the force of air resistance on the object equals the force of gravity pulling it down.
The formula for calculating terminal velocity is: Vt = √(2mg/ρAC), where Vt is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the projected area of the object, and C is the drag coefficient.
The terminal velocity of a lacrosse ball is affected by its mass, the density of air, the cross-sectional area of the ball, and the drag coefficient which depends on the shape and surface roughness of the ball.
The denser the air, the greater the air resistance on the ball, which slows it down and results in a lower terminal velocity. This means that a lacrosse ball will have a lower terminal velocity in higher altitudes where air density is lower.
Yes, the initial velocity of a lacrosse ball can affect its terminal velocity. If the ball is thrown or shot with a higher initial velocity, it will take longer to reach its terminal velocity as it needs to overcome a greater force of air resistance.