Hints offered by K Russell, with video solutions by 'DLBmaths'
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Paper 1
Question 1
Hint 1: Resolve parallel and perpendicular to the plane
Hint 2: Use F = ma
Hint 3: Use a constant acceleration equation
Hint 4: and here is a video of the solution:
Question 2
2a) Hint 1: Use the quotient rule for differentiation
2b) Hint 2: Use the chain rule for differentiation
Hint 3: and here is a video of the solution:
Question 3
Hint 1: Know that acceleration is the derivative of velocity with respect to time
Hint 2: Substitute and find the magnitude
Hint 3: and here is a video of the solution:
Question 4
Hint 1: Draw a diagram showing all the forces and distances from A
Hint 2: Take moments from C
Hint 3: and here is a video of the solution:
Question 5
Hint 1: Write the general form of the partial fractions for an irreducible quadratic factor
Hint 2: Multiply through by the denominator and substitute for x
Hint 3: Make further substitutions to find other constants
Hint 4: and here is a video of the solution:
Question 6
Hint 1: Friction acts vertically and the reaction force acts radially towards the centre of the horizontal circle
Hint 2: Resolve vertically and then horizontally with F = ma
Hint 3: and here is a video of the solution:
Question 7
Hint 1: Use constant acceleration equations vertically and horizontally
Hint 2: Range x = 60 when height y = 0
Hint 3: write horizontal equation in terms of t and substitute into the vertical equation
Hint 4: and here is a video of the solution:
Question 8
Hint 1: Use momentum before collision is equal to momentum after the collision
Hint 2: Use F = ma to find a
Hint 3: Use a constant acceleration equation
Hint 4: and here is a video of the solution:
Question 9
9a) Hint 1: Find the resultant force acting on the body
9a) Hint 2: Integrate the variable force to find work done
9b) Hint 3: Use the Work Energy principle (WD = change in energy)
Hint 4: and here is a video of the solution:
Question 10
Hint 1: Use integration by parts twice
Hint 2: and here is a video of the solution:
Question 11
Hint 1: Differentiate and rearrange to find dy/dx
Hint 2: Substitute x = 2 into the original curve to find y
Hint 3: and here is a video of the solution:
Question 12
12a) Hint 1: Resolve vertically and use Hooke's Law
12b)i) Hint 2: Apply F = ma vertically
12b)i) Hint 3: Rearrange to Simple Harmonic Motion (SHM) equation of motion
12b)ii) Hint 4: Use the formula sheet
12c) Hint 5: Consider when the string is not in tension
Hint 6: and here is a video of the solution:
Question 13
13a) Hint 1: Apply Newton's Inverse Square Law at the surface and at the satellite
13b) Hint 2: Use F = ma
Hint 3: and here is a video of the solution:
Question 14
14a)ii) Hint 1: Find the position vector of each at time t
14b) Hint 2: Find the magnitude of the relative position and equate it to 7
14b) Hint 3: Use the quadratic formula to solve for t
Hint 4: and here is a video of the solution:
Question 15
15a) Hint 1: Use F = ma where a = v(dv/dx)
15b) Hint 2: Separate the variables and integrate
15b) Hint 3: Use the initial conditions to find c
Hint 4: and here is a video of the solution:
Question 16
Hint 1: Find the integrating factor
Hint 2: and here is a video of the solution:
Question 17
17a) Hint 1: Resolve perpendicular and parallel to the plane
17a) Hint 2: Use F = ma
17a) Hint 3: Use a constant acceleration equation
17b) Hint 4: Apply the horizontal force and resolve perpendicular and parallel to the plane
17b) Hint 5: Rearrange to find a in terms of μ
17b) Hint 6: Use a constant acceleration equation
Hint 7: and here is a video of the solution: