A man stands on a ledge and throws a ball into the air so that, at the instant when the ball leaves his hand, the ball is 4 m above the ground and is moving vertically upwards with speed k ms−1k \text{ ms}^{-1}k ms−1. The motion of the ball is modelled as that of a particle moving freely under gravity and the acceleration due to gravity is modelled as being of constant magnitude 10 ms-2. The ball hits the ground T T\,T seconds after leaving the man's hand.
Using the model, find the value of T T\,T in terms of kkk.
197 exam-style questions on Edexcel A Level Maths Constant Acceleration, covering 8.2 Modelling Assumptions, 8.3 Quantities and Units, 8.4 Working with Vectors, 9.1 Displacement-Time Graphs, 9.2 Velocity-Time Graphs, 9.3 Constant Acceleration Formulae 1, 9.4 Constant Acceleration Formulae 2, and 9.5 Vertical Motion Under Gravity. Each one has a worked solution and a mark scheme showing where the marks go.