You want to throw a ball vertically upwards so that it will go up 50 meters before turning around. What initial velocity do you have to give it?
We use the formula for the final velocity in terms of the
initial velocity and height:
vF² = v0² - 19.6h
where v0 represents the original velocity and
vF represents the final velocity.
When the ball reaches its maximum height it must stop at that instant
as it turns around, so we use
vF = 0 and h = 50, and solve for v0
vF² = v0² - 19.6h
0² = v0² - 19.6(50)
0 = v0² - 980
980 = v0²
Taking positive square roots of both sides:
31.3 = v0
So the answer is about 31.3
Edwin