Two motor cars are 1.2 km apart and moving in opposite directions. Car A is moving at 80 km/h due east and car B is moving at 100 km/h due west. Calculate: a) The velocity of car A relative to car B. b) The time taken for the cars to reach each other. c) The distance car A travels to reach car B.

3. Two motor cars are 1.2 km apart and moving in opposite directions. Car A is moving at 100 km/h due east and car B is moving at 80 km/h due west.

Let's define the direction East as positive and West as negative. Velocity of car A ($v_A$) = +100 km/h Velocity of car B ($v_B$) = -80 km/h Distance between cars ($d$) = 1.2 km

a) The velocity of car A relative to car B. Step 1: Use the relative velocity formula. The velocity of car A relative to car B ($v_{AB}$) is given by: $v_{AB} = v_A - v_B$ Step 2: Substitute the given velocities. $v_{AB} = 100 km/h - (-80 km/h)$ $v_{AB} = 100 km/h + 80 \text{ km/h}$ Step 3: Calculate the relative velocity. $v_{AB} = 180 \text{ km/h}$ The velocity of car A relative to car B is $\boxed{180 km/h}$.

b) The time taken for the cars to reach each other. Step 1: Determine the relative speed of approach. Since the cars are moving towards each other, their relative speed of approach is the sum of their magnitudes, which is the magnitude of $v_{AB}$. $v_{rel} = |v_A| + |v_B| = 100 km/h + 80 km/h = 180 \text{ km/h}$ Step 2: Use the formula for time ($t = \frac{distance}{speed}$). $t = \frac{d}{v_{rel}}$ Step 3: Substitute the distance and relative speed. $t = \frac{1.2 km}{180 km/h}$ Step 4: Calculate the time. $t = \frac{1.2}{180} \text{ hours}$ $t = \frac{12}{1800} \text{ hours}$ $t = \frac{1}{150} \text{ hours}$ To express in minutes: $t = \frac{1}{150} \times 60 minutes = \frac{60}{150} minutes = \frac{2}{5} minutes = 0.4 \text{ minutes}$ The time taken for the cars to reach each other is $\boxed{0.4 minutes}$ or $\boxed{\frac{1}{150} hours}$.

c) The distance car A travels to reach car B. Step 1: Use the formula for distance ($d = speed \times \text{time}$). $d_A = v_A \times t$ Step 2: Substitute the velocity of car A and the time calculated in part (b). $d_A = 100 km/h \times \frac{1}{150} \text{ hours}$ Step 3: Calculate the distance. $d_A = \frac{100}{150} \text{ km}$ $d_A = \frac{2}{3} \text{ km}$ The distance car A travels is $\boxed{\frac{2}{3} km}$ or approximately $\boxed{0.667 km}$.

What's next?