For a chance to win the first prize (£100 Amazon voucher), or one of our prizes for runners-up, submit your typed or neatly written solutions of the following problems tophysics@lincoln.ac.ukor by post to Physics Challenge, School of Mathematics and Physics, University of Lincoln, Lincoln, LN6 7TS. Please include your full name, postal address and email, as well as the name and address of your school. The closing date is 5 January, 2017. The competition is open to all young pre-university people in UK aged 16–18 years. It is not open to current university students. See full Terms and Conditions.

1. A log of radius R rolls towards a frog with speed v. What is the minimum upwards velocity u with which the frog has to jump in order to jump over the log? How close can the log get before the frog must begin to jump?

2. The…