I'm having a really hard time figuring out how to solve three word problems from my homework. I think they all have to do with vector addition, but I'm not sure.
1) A person needs to get directly across a river by boat. The boat's speed is 20ft/sec. There is a strong river current of 14ft/sec. Towards what direction should the person head the boat to keep a straight path across the river? What is the magnitude of the resulting velocity vector?
For this one, I don't have a problem finding the angle the boat should travel at.
To get the angle I did:
-20sin(theta) + 14 = 0
sin(theta)= 7/10
0 = arcsin (7/10) = 44.43 degrees
Not really sure how to go about finding the magnitude of the resulting velocity vector. The book says that it should be 14.28ft/sec, but I'm not sure how to get there.
2) Two tractors are pulling a heavy cart to a silo. One of the tractors exerts a force of 4500 pounds and the other exerts a force of 3900 pounds. The pulling ropes define an angle of 46 degrees. Find the magnitude of the resulting force applied to the cart.
For this, I have the components of the first vector T1 as (4500cos(46) , 4500sin(46)), and the components of the second vector T2 as (3900 , 0)
(4500cos(46) + 3900 , 4500sin(46) + 0)
(7025.96 , 3237.03)
I'm supposed to be getting 7735.8lbs as the answer, but I don't see how.
3) A 150lb object is suspended by two ropes. Find the magnitude of the tension on each rope if rope T1 has an angle of elevation of 42 degrees, while T2 hangs at 31 degrees.
Weight = (0, -150)
T1= (-T1cos(42) , T1sin(42))
T2= (T2cos(31) , T2sin(31))
From here I get really lost. I'm supposed to find that T1=134.5 and T2=116.6.
1) A person needs to get directly across a river by boat. The boat's speed is 20ft/sec. There is a strong river current of 14ft/sec. Towards what direction should the person head the boat to keep a straight path across the river? What is the magnitude of the resulting velocity vector?
For this one, I don't have a problem finding the angle the boat should travel at.
To get the angle I did:
-20sin(theta) + 14 = 0
sin(theta)= 7/10
0 = arcsin (7/10) = 44.43 degrees
Not really sure how to go about finding the magnitude of the resulting velocity vector. The book says that it should be 14.28ft/sec, but I'm not sure how to get there.
2) Two tractors are pulling a heavy cart to a silo. One of the tractors exerts a force of 4500 pounds and the other exerts a force of 3900 pounds. The pulling ropes define an angle of 46 degrees. Find the magnitude of the resulting force applied to the cart.
For this, I have the components of the first vector T1 as (4500cos(46) , 4500sin(46)), and the components of the second vector T2 as (3900 , 0)
(4500cos(46) + 3900 , 4500sin(46) + 0)
(7025.96 , 3237.03)
I'm supposed to be getting 7735.8lbs as the answer, but I don't see how.
3) A 150lb object is suspended by two ropes. Find the magnitude of the tension on each rope if rope T1 has an angle of elevation of 42 degrees, while T2 hangs at 31 degrees.
Weight = (0, -150)
T1= (-T1cos(42) , T1sin(42))
T2= (T2cos(31) , T2sin(31))
From here I get really lost. I'm supposed to find that T1=134.5 and T2=116.6.