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Help with Vectors and Relative Velocity

 
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KristinC



Joined: 14 Feb 2011
Posts: 1
Location: Austin, TX

PostPosted: Mon Feb 14, 2011 3:17 am    Post subject: Help with Vectors and Relative Velocity Reply with quote

I have two questions I need help with. I have absolutley no clue how to even begin these:

1. A man points his rowboat north straight across a river width 100 m. The river flows due east. The man starts rowing steadily at .75 m/s and reaches the other side of the river 150 m downstream from his starting point. What is the speed of the river?

2. Airplane 1 flies due east at 250 km/h relative to the ground. At the same time Airplane 2 flies 325 km/h, 35 degrees north of east relative to the ground. What is the velocity of Airplane 1 relative to Airplane 2?

Thanks in advance!
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hepcj
Site Admin


Joined: 23 Jun 2007
Posts: 125

PostPosted: Wed Feb 23, 2011 2:09 pm    Post subject: Reply with quote

For the first problem you need to find the angle that the rower makes when he is crossing the river.
We know the width of the river is 100m and we know he ends up 150m downstream. These two distance form the sides of a right angled triangle.
And using the trigonometric ratio tan = opposite/adjacent.

The angle is = arctan(150/100) = 56.3 deg.

From this information we can calculate the velocity of the river. The rower tried to cross the river by rowing to the other side but the velocity of the water carried him downstream.
From the angle that made from the straight path across the river, we can determine the x-velocity:

vx = .75m/s sin (56.3) = 0.62 m/s

The second question also involves resolving velocity vectors into their components.

To find the velocity of the second plane relative to the first, we need to find the x and y components of the velocity. The x component will be the velocity in the Easterly direction and the y-component will be the velocity in the Northerly direction. The angle between the two velocity vectors is 35 deg.

x-component = 325km/hr cos(35) = 266 km/hr
y-component = 325km/hr sin(35) = 186 km/hr

The relative velocity is from plane 2 point of view is the difference between plane 1 and plane 2 velocities in the x and y directions.

i.e delta vx = 250 - 266 = - 16 km/hr
delta vy = 0 - 186 = - 186 km/hr
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