Question

A cab driver heads south with a steady speed of v₁ =24.0 m/s for t1 =3.00 min, then makes a right turn and travels at v₂ =25.0 m/s for t₂=3.00 min, and then drives northwest at v₃ =30.0 m/s for t₃ =1.00 min. For this 7.00-min trip, calculate the total vector displacement.

Answer 1

The total vector displacement of the cab driver is 177.0 m.

Step-by-step explanation:

To calculate the total vector displacement of the cab driver, we need to find the individual displacements and add them together.

For the first leg of the trip, the cab driver travels south with a speed of 24.0 m/s for 3.00 min. The displacement in this direction can be calculated as:

displacement₁ = (speed₁)(time₁) = (24.0 m/s)(3.00 min) = 72.0 m

For the second leg, the cab driver travels at a speed of 25.0 m/s for 3.00 min. Since the direction is not mentioned, we assume it to be east. The displacement in this direction can be calculated as:

displacement₂ = (speed₂)(time₂) = (25.0 m/s)(3.00 min) = 75.0 m

For the third leg, the cab driver travels northwest with a speed of 30.0 m/s for 1.00 min. The displacement in this direction can be calculated as:

displacement₃ = (speed₃)(time₃) = (30.0 m/s)(1.00 min) = 30.0 m

To find the total displacement, we need to add the individual displacements:

total displacement = displacement₁ + displacement₂ + displacement₃ = 72.0 m + 75.0 m + 30.0 m = 177.0 m