Practice Problems 5. A car moving east at 45 km/h turns and travels west at 30 k

Question

Practice Problems 5. A car moving east at 45 km/h turns and travels west at 30 km/h. 6. You are riding in a bus moving slowly through heavy traffic at 7. A motorboat heads due east at 11 m/s relative to the water What are the magnitude and direction of the change in velocity 2.0 m/s. You hurry to the front of the bus at 4.0 m/s relative to the bus. What is your speed relative to the street? across a river that flows due north at 5.0 m/s. What is the velocity of the motorboat with respect to the shore? 8. A boat is rowed directly upriver at a speed of 2.5 m/s relative to the water. Viewers on the shore find that it is moving at only 0.5 m/s relative to the shore. What is the speed of the river? Is it moving with or against the boat? 9. An airplane flies due north at 150 km/h with respect to the air. There is a wind blowing at 75 km/h to the east relative to the ground. What is the plane's speed with respect to the ground? 10. An airplane flies due west at 185 km/h with respect to the air. There is a wind blowing at 85 km/h to the northeast relative to the ground. What is the plane's speed with respect to the ground? .l Section Review is the distance you walk equal to the that vector additio

Explanation / Answer

6.

Speed of you w.r.t to street = speed of you w.r.t bus + speed of bus w.r.t. street

Vys = Vyb + Vbs

Given that

Vyb = 4 m/sec

Vbs = 2 m/sec

So,

Vys = 4 + 2 = 6 m/sec

8.

Speed of boat w.r.t to ground = speed of boat w.r.t water + speed of water w.r.t. ground

Vbg = Vbw + Vwg

Now we need

Vwg = Vbg - Vbw

Given that

Vbg = 0.5 m/sec

Vbs = 2.5 m/sec

So,

Vwg = 0.5 - 2.5 = -2 m/sec

Since Velocity of water is negative so it's moving against the boat.

10.

Speed of plane w.r.t to ground = speed of plane w.r.t air + speed of air w.r.t. ground

Vpg = Vpa + Vag

Given that

Vpa = 185 km/h due west = (-185 km/h) i

Vag = 85 km/h due northeast (at 45 deg from +x-axis CCW)

Vag = 85*cos 45 deg i + 85*sin 45 deg j

Vag = 60.1 i + 60.1 j

So,

Vpg = Vpa + Vag

Vpg = -185 i + (60.1 i + 60.1 j)

Vpg = -124.9 i + 60.1 j

So final speed of plane w.r.t to ground will be

|Vpg| = sqrt ((-124.9)^2 + 60.1^2) = 138.6 km/hr

Direction = arctan (60.1/124.9) = 25.7 deg North of west

Final speed = 138.6 km/hr due 25.7 deg North of West

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