Section 1.7: Mixed Practice

This section provides a collection of mixed problems from previous sections, combining 1D/2D motion, vectors, projectile motion, and derivatives of position to strengthen problem-solving skills.

Example 1

A projectile is launched at 20 m/s at 30°. Find horizontal and vertical components of velocity, max height, and range.

v_x = 20 cos30° ≈ 17.32 m/s

v_y0 = 20 sin30° = 10 m/s

H = v_y0² / 2g = 10² / (2*9.8) ≈ 5.10 m

Time of flight t_f = 2*v_y0/g ≈ 2.04 s

Range R = v_x * t_f ≈ 35.3 m

Example 2

A particle moves along x-axis: x(t) = 3t² – 2t. Find velocity and acceleration at t = 4 s.

v(t) = dx/dt = 6t – 2 → v(4) = 6*4 – 2 = 22 m/s

a(t) = dv/dt = 6 → a(4) = 6 m/s²

Practice Problems

  1. Projectile launched at 15 m/s at 45°. Compute components, max height, range, and time of flight.
  2. Block slides down 25° frictionless incline of 6 m. Find acceleration and time to reach bottom.
  3. Position function x(t) = 2t³ – 5t. Find v(t) and a(t) at t = 2 s.
  4. Projectile fired horizontally from 18 m height at 12 m/s. Determine landing distance and time.
  5. Particle moves with r(t) = (t², t³). Find velocity and acceleration at t = 3 s.
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