Question

"a ball is thrown upwards with initial velocity 20 m/s. After reaching maximum height, on the way down it strikes a bird which is 10 m above the ground. What is the velocity of the ball when it hits the bird?"

I know acceleration would be -9.8 m/s^2 (to assume free fall), the initial velocity would be 20, and that the final position would be 10, but I don't know how to find the max height to then use to find the final velocity. thank you

Answer 1

Just set this up as a quadratic function. I assume that we start from a height of zero, since you don't say.
h(t) = 20t - 4.9t^2
Now, you want to solve
20t - 4.9t^2 = 10
t = 0.583, 3.498
Since v=20-9.8t, that would make
v(3.498) = 20-9.8*3.498 = -14.28

You don't need to find the max height for this problem, but that occurs when v=0. So, h(2) = 20.4

Answer 2

Ohhh ok. Thank you so much! :D