You have two equations:
Equation #1: x(t) = v0·cos(θ) gives the x-value, which is a horizontal value
Equation #2: y(t) =v0·sin(θ) - 16t² gives the y-value, which is a vertical value
Question 1) says that the height is 4.7; this is a y-value, specifically y(1).
It also gives you the time, t = 1, and gives you the initial velocity, v0 = 25.
You now have the equation: y(1) = 4.7 = 25sin(θ) - 16(1)²
Question 2) Solve the equation from question 1, for θ.
Question 3) You are again looking for height: use y(t) =v0·sin(θ) - 16t²; entering, .5 for t, 25 for v0, and your answer for question 2 for θ. Solve for y(.5).
Question 4) I'm assuming, possibly incorrectly, that they want the x-value after 1 second. Use the first equation, substituting the values for v0 and θ.
Question 5) Redo question 2, but using 5.2 for y(t), 1 for t, and 28 for v0.
Question 6) Redo question 3, but using 28 for vo, .5 for t, and you answer for question 5 for θ.
Question 7) Redo question 4, for the numbers for Jon.
Question 8) Redo question 3 using the new number.
If you need more help, repost where your questions are.