Problem: A physics teacher is designing a ballistics event for a science competition. The ceiling is 3.00 m high, and the maximum velocity of the projectile will be 20.0 m/s.

a) What is the maximum initial velocity in the vertical direction that the projectile could have?

 

So I think that the max velocity of a projectile will always be when it is launched or right before it hits the ground, so wouldn't the answer be 20.0 m/s? If you point the cannon or whatever is launching the projectile vertically upwards with no tilt, there would be 0 horizontal velocity, so wouldn't all the velocity be in the vertical direction?

But the answer is apparently 7.68 m/s, which I don't understand.

Essentially it's asking for the maximum angle the projectile can be launched from without it hitting the ceiling. But instead of the angle, they want the y-component of the initial velocity. (The two are related!) The initial speed of the projectile is 20 m/s, but what is its initial y-component of velocity?

Oh, I see now! I didn't realize that it couldn't hit the ceiling, so there must be an angle.

I was able to calculate the answer now. Thanks!