FYKOS Year 30 Series 1 Problem 5 — On a walk · FYKOS 30 #30.1.5

Physics · mechanics

Problem

Katka decided to go for a walk with her pet rat. They arrived on a flat meadow and when the rat was at a distance x1=50  mx_{1}=50\;\mathrm{m} from Katka, she threw him a ball with the speed v0=25  m⋅s−1v_{0}=25\;\mathrm{m}\cdot \mathrm{s}^{−1} and an angle of elevation α0α_{0}. In that moment, he started running towards her with the speed v1=5  m⋅s−1v_{1}=5\;\mathrm{m}\cdot \mathrm{s}^{−1}. Find a general formula for an angle φφ as a function of time, where the angle φ(t)φ(t) is the angle between the horizontal plane and the line between the rat and the ball. Draw this function into a graph and, based on the graph, determine, whether it's possible for the ball to obscure the Sun for the rat, when the Sun is situated φ0=50°φ_{0}=50° above the horizon in the direction of the running rat. Use the acceleration due to gravity g=9.81  m⋅s−2g=9.81\;\mathrm{m}\cdot \mathrm{s}^{−2} and for simplicity imagine we are throwing the ball from a zero height.

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