Consider an antelope being chased by a tiger. The antelope is running at a veloc
ID: 2068034 • Letter: C
Question
Consider an antelope being chased by a tiger. The antelope is running at a velocity of 5.95 m/s at an angle 16.1 degree E of S. The tiger is running at a velocity of 11.47 m/s at an angle of 30.0 degree W of S. (Use East as positive x and North as positive y) What are the x and y components of the antelope's velocity with respect to the ground? What are the x and y components of the tiger's velocity with respect to the ground?What are the x and y components of the velocity of the tiger with respect to the antelope? What is the magnitude of the velocity of the tiger with respect to the antelope?If the tiger and the antelope are 174 m apart, how long will it take the tiger to catch the antelope?Explanation / Answer
Va = 5.95 m/s at an angle 16.1 degree E of S Vt = 11.47 m/s at an angle of 30.0 degree W of S (Use East as positive x and North as positive y) For antelope, Vx = 5.95sin16.1 = 1.65 m/s Vy = -5.95cos16.1 = -5.72 m/s For tiger, Vx = 11.47sin30 = 5.74 m/s Vy = -11.47cos30 = -9.93 m/s Tiger with respect to antelope, Vtrela = Vt - Va hence, Vxrel = 5.74 - 1.65 = 4.09 m/s Vyrel = -9.93 + 5.72 = -4.21 m/s Now, mag Vtrela = sqrt(4.09^2 + 4.21^2) = 5.87 m/s Now if distance d =174 m speed = distance / time or, time = distance / speed or, time = 174 / 5.87 or, time = 29.64 s