QCEVault

Vectors and matrices — Question 19

QCAA 2020, Paper 2 · 7 marks

Q19 · 2020 · Technology-activeComplex unfamiliar7 marks

QUESTION 19 (7 marks)

An object is swinging at the end of a 0.5 m length of string in a vertical circular path with a constant angular speed, completing each revolution in 0.24 seconds. The object is projected from a height of 0.3 m above the ground in a vertical plane and just passes over a narrow pole as shown in the diagram. The pole is 2.05 m high and its base is 14 m horizontally from where the object was projected. A flat-topped vehicle of length 0.6 m and height 0.4 m is initially at rest against the pole as shown. At the instant that the object is projected, the vehicle moves in a horizontal direction away from the pole in the same vertical plane with an acceleration of magnitude aa m s−2^{-2}. The object strikes the middle of the top of the vehicle. Assuming that air resistance is negligible, use vector calculus to model the motion of the projectile in the vertical plane and determine aa.
Projectile setup with swing, pole and accelerating vehicle
Question linkOriginal paper

Related questions

  1. Q2 · 2025 QCAA · Paper 1 · 1 mark
    The position vector of a particle at time tt is given by r=sin⁡(t)i^+cos⁡(t)j^\mathbf r=\sin(t)\hat{\mathbf i}+\cos(t)\hat{\mathbf j}. The path of the particle is
    Vectors and matrices
  2. Q6 · 2025 QCAA · Paper 1 · 1 mark
    At time tt, a particle travels with a velocity of v=(21+t2)i^−2tj^\mathbf v=\left(\dfrac{2}{1+t^2}\right)\hat{\mathbf i}-2t\hat{\mathbf j}. Determine a general expression for the position vector, r\mathbf r, of the particle during this motion.
    Vectors and matrices
  3. Q8 · 2025 QCAA · Paper 1 · 1 mark
    The position vectors of two objects over time, tt, where t≥0t\ge0, are given by r1(t)=−2i^+t2j^\mathbf r_1(t)=-2\hat{\mathbf i}+t^2\hat{\mathbf j} and r2(t)=ati^+4j^\mathbf r_2(t)=at\hat{\mathbf i}+4\hat{\mathbf j} (where a∈Ra\in\mathbb R). Given that the two objects collide, the value of aa is
    Vectors and matrices
  4. Q11 · 2025 QCAA · Paper 1 · 5 marks
    Consider the system of linear equations represented using the augmented matrix shown. [1−1−1−6−21110044]\left[\begin{array}{ccc|c}1&-1&-1&-6\\-2&1&1&1\\0&0&4&4\end{array}\right] Key: R1R_1 represents the row 1 values.
    Vectors and matrices