Final answer:
By using the impulse-momentum theorem, which relates impulse (force × time) to change in momentum (Δp = mΔv), we calculate the mass of the lacrosse ball to be 32 kg after being thrown with a 2000 N force for 0.8 seconds, resulting in a 50 m/s velocity change.
Step-by-step explanation:
To find the mass of the ball in a lacrosse game where a force of 2000 N is applied for 0.8 seconds resulting in a change in velocity (Δv) of 50 m/s, we can use the impulse-momentum theorem. The impulse-momentum theorem states that the impulse (force × time) on an object is equal to the change in its momentum (Δp), which can also be written as the mass (m) times the change in velocity (Δv) since momentum p = mv. Therefore, the formula to find the mass is:
m = Δp / Δv
The impulse (I) is the product of the force (F) and the time (t) during which the force acts:
I = F × t = 2000 N × 0.8 s = 1600 N·s
Now we can use the impulse and the change in velocity to find the mass:
m = I / Δv = 1600 N·s / 50 m/s = 32 kg
Therefore, the mass of the lacrosse ball is 32 kg.