Your answer to a) is incorrect, as you are taking the total initial velocity of the ball, instead of only the vertical component. If the ball was kicked directly up at 30ms
-1, then your answer would be correct but it is instead being kicked at an angle.
As to picking the formula, it is very, very important to remember that your standard motion formulas only apply in one dimension. This question is in two dimensions, so you need to split it up into two separate axises; the vertical, and the horizontal. I find it easy to figure out which formula to use when I organise them like this (a cheat sheet is always handy in this course, this was on my one):
The 5 variables: u, v, a, t, and s (also could be x, d, l, or anything meaning displacement)
The 5 formulas:
v = u + at (No s in formula)
s = 0.5t(u + v) (No a in formula)
s = ut + 0.5at
2 (No v in formula)
s = vt - 0.5at
2 (No u in formula)
v
2 = u
2 + 2as (No t in formula)
So, whenever you have a question, list out which three variables you know, and the variable you need to solve for. You will have one variable that you don't know and don't need to know, which you can use to find which formula to use. I find this much easier than trying to find which formula has all four variables the scenario calls for.
Using this method to solve your problem is easy. For part a), you don't know the initial vertical velocity, because you don't know the angle. You know the final vertical velocity is 0 (this is at the top of the path), and that a is equal to g (g is normally -10, because in many questions displacement upwards is positive [though if you define displacement downwards to be positive, then g is positive]). The question says that the time is 5 seconds, but you know that it only takes half that time for the ball to reach the highest point, so t = 2.5. And finally, what you need to find is s, the maximum heigh reached.
The one variable that is irrelevant to this equation is u. You don't know what it is, and you don't need to find it. So, the equation we'll use is:
s = vt - 0.5at
2Sub in your variables:
s = 0*2.5 - 0.5(-10)*2.5
2s = 5*6.25
s = 31.25 m
That's your answer to a), now for b). We must first find the vertical component of the ball's initial velocity. We want to find u, we know that t = 2.5 as before, s = 31.25 as previously solved, that v = 0, and that a = -10. In this case, we can involve all 5 variables, so we can pick any equation we like, as long as it has u in it (as we are solving for u). Let's use this one, as it's damn simple:
v = u + at
0 = u + -10(2.5)
u = 25 ms
-1As we now know the vertical initial velocity, and the full initial velocity, we can use trig to solve the angle. Draw a right angle triangle with its right angle on the bottom right. The vertical side has a magnitude of 25, and the hypotenuse has a magnitude of 30.
sin(theta) = 25/30
theta = sin
-1(5/6)
theta = 56
oI hope this helps, it ended up being rather lengthy
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