Optimizing Projectile Motion: Strategies for Navigating a River with a Boat

[ff4930]

A river is 0.76 km wide. The banks are straight and parallel. The current is 4.0 km/h and is parallel to the banks. A boat has a maximum speed of 3.0 km/h in still water. The pilot of the boat wishes to go on a straight line from A to B, where AB is perpendicular to the banks. What should the pilot do?

a-Take none of these actions.
b-Head 22° upstream from the line AB.
c-Give up-the trip from A to B since it is not possible with this boat.
d-Head directly across the river.
e-Head 68° upstream from the line AB.

What I did:
Since I know it forms a right triangle where
angle theta is unknown
4km/h is the adjacent and .76km is the opposite

so I did inverse tan 4/.76 and got 79 degrees.
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Which of the following statements are true? (Select all that apply and ignore any effects due to air resistance.)

a-When a projectile is fired horizontally from a certain height, it has a higher speed upon reaching the ground than does an identical projectile dropped from rest from the same height.

b-None of these statements are true.

c-When a projectile is fired from a certain height at an upward angle, it takes longer to reach the ground than does an identical projectile dropped from rest from the same height.

d-When a projectile is fired horizontally, it takes the same amount of time to reach the ground as an identical projectile dropped from rest from the same height.

I chose C & D but it was wrong.
I chose C because if shot in an upward, it takes extra time to reach its highest point where velocity is 0, then from there is the same as dropping from rest.

I chose D because the only acceleration is from gravity so it would take the same amount of time to reach the ground.

Am I wrong?

 

[Redbelly98]

A river is 0.76 km wide. The banks are straight and parallel. The current is 4.0 km/h and is parallel to the banks. A boat has a maximum speed of 3.0 km/h in still water. The pilot of the boat wishes to go on a straight line from A to B, where AB is perpendicular to the banks. What should the pilot do?

a-Take none of these actions.
b-Head 22° upstream from the line AB.
c-Give up-the trip from A to B since it is not possible with this boat.
d-Head directly across the river.
e-Head 68° upstream from the line AB.

What I did:
Since I know it forms a right triangle where
angle theta is unknown
4km/h is the adjacent and .76km is the opposite

No, those values don't have the same units (km/h vs. km). So it doesn't make sense to use them to draw a triangle.

Draw the triangle using the given velocities pointing in the appropriate directions.

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Which of the following statements are true? (Select all that apply and ignore any effects due to air resistance.)

a-When a projectile is fired horizontally from a certain height, it has a higher speed upon reaching the ground than does an identical projectile dropped from rest from the same height.

b-None of these statements are true.

c-When a projectile is fired from a certain height at an upward angle, it takes longer to reach the ground than does an identical projectile dropped from rest from the same height.

d-When a projectile is fired horizontally, it takes the same amount of time to reach the ground as an identical projectile dropped from rest from the same height.

I chose C & D but it was wrong.
I chose C because if shot in an upward, it takes extra time to reach its highest point where velocity is 0, then from there is the same as dropping from rest.

I chose D because the only acceleration is from gravity so it would take the same amount of time to reach the ground.

Am I wrong?

C & D are correct, as you have reasoned out. That makes B false.

Now think about whether A is true or false.

 

[ff4930]

oh wow, thanks for pointing it out, I feel so dumb hahah.
Boat cannot make it if max. speed is 3km/h.
and for number 2- after thinking, A is correct.

Thanks for your help.

I have another question where it is half done.On a carousel a person has an acceleration of magnitude of 0.86 m/s2 when she is standing 4.3 m from the axis.
(a) What is the period of the person on the carousel?
14.2s
(b) What is the speed of the person on the carousel?
1.9m/s
(c) What are her acceleration magnitude and the speed if she then moves to a distance of 2 m from the carousel center and the carousel keeps rotating with the same period?

acceleration magnitude
speed

Ive used the acceleration formula A = v^2/R and Period formula 2piR/T for questions A and B

I don't understand Question C. Can someone explain?

 

[ff4930]

Can someone please help, I got half of this, but I don't get what the 2nd part of question asks. If she moves to a distance 2m from the carousel center meaning raidus is 6.3? I tried the same formula but didn't work.

 

[alphysicist]

Hi ff4930,

Can someone please help, I got half of this, but I don't get what the 2nd part of question asks. If she moves to a distance 2m from the carousel center meaning raidus is 6.3? I tried the same formula but didn't work.

It reads to me like she is moving to a position that is 2m from the carousel center, not that she is moving an additional 2m away. She was 4.3m from the axis, now she has moved so that she is 2m from the axis.

 

[ff4930]

Hi, thanks for replying, I seem to get it.
2/4.3 * acc
2/4.3 * 1.9

thank you!