Resolving Vector Problems: Finding Solutions to Confusing Questions

[Acidvoodoo]

resolving vectors problems

hello, i have some questions to do but am unsure where to start on some of them, the first one is

[assume the Earth's gravitational pull is 10n]

1)"A motor vessel tows a small dinghy by a rope which makes an angle of 20 degrees to the horizontal. The Tension in the rope is 150n"

a)what is the value of the force that pulls the dingy in the forwards direction?
b)what is the value of the vertical force lifting the bows out of the water? [i don't know what bows is maybe the sheet hasa typo and it means boats?

2)a garden roller has a mass of 70kg. A man exerts a force of 200n on it at an angle of 45 degrees to the ground.
Find the verticle force of the roller on the ground:
a)if he pulls the roller
b)if he pushes the roller

4)a river is 50m wide. A rowing boat sets off across the river aiming for a point on the opposite bank perpendicularly opposite the starting point. However, as a result of the the current in the river, the boat actually ends up 30m downstream of the intended landing point. It takes 75s for the boat to cross the river.

a)What distance does the boat actually travel
b)what is the resultant velocity of the boat
c)what is the velocity of the current in the river? [assume the current is the same at all points in the river
d)with what speed would the boat move in still water?

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for question 1a, i didn't understand what it meant by "to the horizonal", but anyway i drew a little diagram and used Sin=O/H , rearranged to Sin*H=O to get Sin20*150=136.84n [tp 2 dp]

for question b i had no idea what it means

for question 2 i tried drawing a sketch but am not sure what to do. the garden roller must exert a 700n force to the ground, and the man a 200n at a 45 degree again, but then the question just confuses me by asking what direction he is pushing or pulling, as if he pulls the roller isn't he no longer exerting the 200n force upon the mower, ahh I'm confused

for question 4a i used pythagoras to get 50^2+30^2= sqrt:3400which is 58.30m two dp

for b i used just speed=distance/time but i don't think that is the correct choice of equation [bit too basic, I'm not sure?] but anyway i got 0.77m/s for that one

for c) and d) i have no idea where yo start?


can anyone offer any points to get me started on thw questions I'm stuck on [as well as seeing if my existing aswers are correct?]

thanks if you can help :D

 

[HallsofIvy]

This dingy is much smaller than the boat. Your picture should have had a line representing the rope coming down toward the dingy. Draw a horizontal line from the point where the rope meets the dingy. The angle is 20 degrees. A vertical line will complete the right triangle. Yes, you are correct, the force pulling the dingy along is represented by the horizontal line so it is 150 cos(20).

The "bow" of a boat is its front end (yes, people will actually expect you to know things like that- read, read, read!), the "bows" (plural) are the two sides of the front of the boat. In any case, since it said "vertical force lifting" you should immediately think of the vertical line in your right triangle and therefore of sin(20).

" the garden roller must exert a 700n force to the ground, " Are you using g= 10? 9.8 is a more common figure.

"if he pulls the roller isn't he no longer exerting the 200n force upon the mower?" Why would you think that. Whether you are pushing down or lifting up, you are exerting a force. Since the handle is coming up from the roller, if he is pushing the handle he is pushing DOWN on the roller. If he is pulling the handle, he is lifting up on the roller. Since you know the angle, you can calculate the horizontal and vertical components.

4 a and b you have exactly correct (even if you think it is too basic!).

for 4c, just remember that the current goes DOWNSTREAM while the boat was being steered directly across the river. You know that the boat drifted 30 m down stream in 75 s. What speed is that?

for 4c, the boat went 50 m across the river in 75 s. If there were no current, it would have gone straight there (without drifting down stream) What speed is 50 m in 75 s?

 

[M98Ranger]

Hello there,

It seems like you are having trouble with some vector problems. Don't worry, these types of problems can be confusing at first but with some practice, you will get the hang of it.

First, let's start with question 1a. The angle of 20 degrees to the horizontal is referring to the angle the rope makes with the ground. To find the value of the force pulling the dinghy in the forward direction, we can use the formula Tension = Force * sine(angle). So, in this case, the force we are looking for is the force in the x-direction, which is the forward direction. This can be found by using the formula as follows: 150 = F * sin(20). Rearranging the equation, we get F = 150/sin(20) = 441.21 N. So, the value of the force pulling the dinghy in the forward direction is 441.21 N.

For question 1b, the vertical force lifting the bows (which means the front of the boat) out of the water can be found by using the formula Tension = Force * cosine(angle). In this case, the force we are looking for is the force in the y-direction, which is the upward direction. So, the equation would be 150 = F * cos(20). Rearranging the equation, we get F = 150/cos(20) = 157.35 N. Therefore, the value of the vertical force lifting the bows out of the water is 157.35 N.

Moving on to question 2, the direction in which the man is pushing or pulling the garden roller does not affect the force he is exerting on it. The magnitude of the force exerted by the man is still 200 N. So, for both parts a and b, the vertical force of the roller on the ground can be found by using the formula F = mg, where m is the mass of the roller and g is the gravitational acceleration (10 m/s^2). Therefore, the vertical force of the roller on the ground is 700 N.

For question 4a, you are correct in using Pythagoras theorem to find the distance the boat actually travels. The distance can be found using the formula d = sqrt(50^2+30^2) = 58.30 m. Good job!

For question 4b, the resultant velocity of the boat