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:

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