Answer:
Final velocity = -39.2 m/s
Step-by-step explanation:
Under the assumption that the ball is in freefall, falling without air resistance, we can use the kinematic equation:
Δx = v₀t + 1/2 * a * t²
Δx = total displacement of the ball
v₀ = initial velocity of the ball
a = acceleration, in this case gravity
t = time in seconds
In our case we need to solve for time so our equation would look like:
0 = (39.2 m/s) * t + (1/2)(-9.81 m/s²) * t²
To solve this equation we can factor out a t from both sides and be left with:
0 = t * (39.2 - 4.905t)
4.905t = 39.2
t = 7.992 and 0
And so our solutions would be t = 0 and 7.992 seconds, meaning the ball has been displaced zero meters at both of these times.
Now, if we were to plug our second answer, 7.992 into a different kinematic equation:
v = v₀ + at
v₀ = initial velocity
a = acceleration, which is still gravity
t = time in seconds
v = 39.2 + (-9.81 * 7.992)
v = -39.2 m/s
Now this was the lengthy way to solve for this problem, however, generally in physics problems where an object is in freefall, aka not facing air resistance, and returns to the same height at which it began, the final velocity is equal in magnitude to the initial velocity at which it was thrown, but has the opposite sign.