How would you calculate the vertical and horizontal components of the velocity of an object with an initial velocity of 15m/s which is travelling upwards at an angle of 30 degrees to the horizontal?

With these sort of questions involving components, I would always advise drawing a diagram of the problem so that you're clear of the situation!In this case we have an object that is travelling at a speed of 15m/s in an upward direction that is 30 degrees to the horizontal.To start, I would draw two lines on the original diagram to show the vertical and horizontal components of this velocity (also label these lines to represent what they are!). I would then take the two lines and the line representing the initial velocity to form a right-angled triangle with an angle of 30 degrees.For this question, we want to calculate these lines that represent the vertical and horizontal velocity components.Instead of me giving the answer straight away, I would ask the student if they have any suggestions as to how to continue with the problem, providing hints as to what the next step would be.In this case, as we know the initial velocity and the angle, we can use the Trigonometric relations to calculate the horizontal and vertical velocity components (similar sort of problem you'd find in GCSE Maths).To find the horizontal component, we'd use the relation cos(theta) = adjacent/hypotenuse; in this case the adjacent is the horizontal component, the hypotenuse is the initial velocity of 15m/s and theta is the angle. You would then rearrange to solve for the horizontal component.To find the vertical component, we'd use the relation sin(theta) = opposite/hypotenuse; in this case the opposite is the vertical component and the hypotenuse is the initial velocity and solve for the vertical component.For this particular question:Vertical component = 7.5m/sHorizontal component = 13.0m/sI would highly encourage the student to ask questions at any time during the lesson if they are unsure of anything relating to the topic.