A particle is projected vertically upwards with speed 20 m s−1^{-1}−1. While it is moving upwards, the resistance has magnitude mv2\dfrac{mv}{2}2mv N, where m m\,m kg is the mass of the particle and v v\,v m s−1^{-1}−1 is its upward velocity.
Use g=9.8g=9.8g=9.8 m s−2^{-2}−2 and take upwards as positive.
Form a differential equation for vvv.
Find v v\,v in terms of t t\,t while the particle is moving upwards.
Find the time taken to reach the greatest height.
91 exam-style questions on WJEC A Level Maths 4.6 Integration (A-level only), covering 4.6.1 Integration (A-level only) and 4.6.2 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.