Determine the initial position components.

Step 1: Determine the initial position components. The aircraft is 60 km north-east from OR Tambo. This means it is at an angle of 45^ from the East (or North). x_0 = 60 (45^) = 60 × sqrt(2)2 = 30sqrt(2) ≈ 42.426 km y_0 = 60 (45^) = 60 × sqrt(2)2 = 30sqrt(2) ≈ 42.426 km Step 2: Calculate the displacement due to flight. The aircraft flies north for 6 hours at a velocity of 96 km/h. D_f = velocity × time = 96 km/h × 6 h = 576 km (North) Step 3: Determine the final position (displacement) from OR Tambo. The final position components are the sum of the initial position and the flight displacement. x_final = x_0 = 42.426 km y_final = y_0 + D_f = 42.426 km + 576 km = 618.426 km The magnitude of the final position is: R = sqrt(x_final)^2 + y_final^2 = sqrt((42.426)^2 + (618.426)^2) R = sqrt(1799.96 + 382450.6) = sqrt(384250.56) ≈ 619.88 km The direction of the final position is: = (y_finalx_final) = ((618.426)/(42.426)) = (14.575) ≈ 86.06^ The position is 86.06^ North of East. The final answer is 619.88 km at 86.06^ North of East. Step 4: Calculate the relative velocity of hoist K to hoist L (Question 1.2.1). Let upward be the positive direction. Velocity of hoist K (descending): V_K = -6.48 km/h Velocity of hoist L (ascending): V_L = +5.04 km/h The velocity of hoist K relative to hoist L is: V_KL = V_K - V_L = -6.48 km/h - (+5.04 km/h) = -11.52 km/h The magnitude is 11.52 km/h and the negative sign indicates a downward direction. The final answer is 11.52 km/h downward. Step 5: Calculate the relative velocity of hoist L to hoist K (Question 1.2.2). The velocity of hoist L relative to hoist K is: V_LK = V_L - V_K = +5.04 km/h - (-6.48 km/h) = 5.04 km/h + 6.48 km/h = +11.52 km/h The magnitude is 11.52 km/h and the positive sign indicates an upward direction. The final answer is 11.52 km/h upward. Step 6: Calculate the maximum height reached by the stone (Question 1.3.1). Given: initial velocity v_0 = 42 m/s, angle = 26^, g = 9.8 m/s^2. The formula for maximum height is: H = ((v_0 )^2)/(2g) H = ((42 26^)^2)/(2 × 9.8) H = ((42 × 0.43837)^2)/(19.6) = ((18.4095)^2)/(19.6) H = (338.909)/(19.6) ≈ 17.29 m The final answer is 17.29 m. Step 7: Calculate the horizontal displacement of the stone (Question 1.3.2). The formula for horizontal range is: R = (v_0^2 (2))/(g) R = ((42)^2 (2 × 26^))/(9.8) R = (1764 (52^))/(9.8) R = (1764 × 0.78801)/(9.8) = (1390.07)/(9.8) ≈ 141.84 m The final answer is 141.84 m. Send me the next one 📸