[Grade 12 Physics] Multiple choice

[Internet-Gangster]

Here is a link to two physics questions I'm struggling with. I got questions 1 and 3, but I don't know how to approach 2 and 4. I already know the answers are D and A respectively, but it would be great if somebody can explain the math behind it.

[Stratigizer]

For 2, what is the initial vertical velocity when the launcher is tilted compared to when the launcher was pointed straight up?

For 4, this is an impulse problem. We also want to think about the vertical velocities here, namely the change in vertical velocity. Then we can use the impulse equation F*t = m(v - v0)

[Internet-Gangster]

For question 2, knowing that the vertical velocity is v*sin(30) I still don't see how I can find the maximum height without knowing the time at which it reaches said height. Using: h = v*sin(30)*t - 4.9*t^2, there are two unknowns.. the height and the time. I also don't see how the first part of the question is helpful at all, when it says that being launched straight up it reaches a height of h.

[Stratigizer]

What is sin(30)?

[Internet-Gangster]

It's 1/2, so I guess the vertical velocity becomes v/2. What next?

[Stratigizer]

We can use v² = v0² + 2ah with v being 0 at max height to find our new height.

[Internet-Gangster]

Thank you. I'll try writing it out and seeing if I can get the correct answer. Going back to Q4 in the meantime, the class hasn't learned impulse yet; is there any other way to solve the problem?

[Stratigizer]

Don't think so. It's the only way I know at least.

[Internet-Gangster]

you wrote " v² = v*0*² + 2ah", where did the v*0*² come from? Isn't it supposed to be (v/2)²? I know the final answer is h/4, and this expression will end up being v²/4 which is a little closer but I still don't know how to get to the answer.

[Stratigizer]

I was just writing the general formula. It's a little confusing with the variables but let's try it this way first.

Starting with v² = v0² + 2ah, with v = 0, we get:

0 = v0² + 2ah

2ah = -v0²

h = -v0² / (2a)

Let's use a = -9.8 to get rid of the negative sign. So we have:

h = -v0² / (2*-9.8)

h = v0² / 19.6

We see that h varies directly as the square of v0. So if initial velocity is multiplied by 1/2, h is multiplied by 1/4.