Projectile Motion #3: Cross River in 47s at 3.64 m/s

In summary: That's what C is asking. And then D is asking for the angle he should point the boat in order to land directly across from the starting point. Does that make sense?In summary, a boat traveling at a speed of 3.4 m/s in still water is faced with a river that is 160 m wide and has a current of 1.3 m/s flowing due West. When the boat points its bow directly across the river, it will travel at a speed of 3.64 m/s relative to the shore and it will take 47.0588 seconds to cross the river. In order to arrive at a point directly across from the starting point, the boat should be pointed at an angle
  • #1
Kildars
95
0
A boat can travel at a speed of 3.4 m/s in still water. A river that is 160 m wide has a current that flows 1.3 m/s due West.

a) If the boat points its bow directly across the river, how fast does the boat travel relative to the shore?
3.64 m/s
b) How long will it take to cross the river?
47.0588 s
c) Fow far downriver will it land (the distance on the bank from the point directly across from the starting point to the landing point)?
m
d) At what angle should the boat be pointed in order to arrive at a point directly across from the starting point? Assume North is directly across the river.
° E of N
e) How long does that take?
s

I got A and B but I don't know how to setup C -- Any ideas?
 
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  • #2
How fast is the boat going downstream? How far does it get in the time it takes to cross the river?
 
  • #3
He's moving 3.4 + 1.3 so 4.5 m/s downstream and it would take him 47.0588 s to get across according to B.
 
  • #4
Doc?! You there?
 
  • #5
Kildars said:
He's moving 3.4 + 1.3 so 4.5 m/s downstream
No, he's moving 3.4 m/s across and 1.3 m/s downstream. (He points the boat directly across, which gets him across in the quickest time possible but requires him to move downstream along with the current. If he wants to go straight across the river without being dragged by the current, he'll have to point the boat at an angle--that's part d.)
and it would take him 47.0588 s to get across according to B.
Right, so how far does he get downstream in that time?
 

Related to Projectile Motion #3: Cross River in 47s at 3.64 m/s

What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity. It follows a curved path, known as a parabola, due to the downward acceleration of gravity.

What factors affect projectile motion?

The factors that affect projectile motion include initial velocity, angle of launch, air resistance, and the acceleration of gravity.

How do you calculate the distance traveled in projectile motion?

The distance traveled in projectile motion can be calculated using the formula: d = v*t, where d is the distance, v is the initial velocity, and t is the time.

What is the formula for calculating the time of flight in projectile motion?

The formula for calculating the time of flight in projectile motion is: t = 2*v*sin(theta)/g, where t is the time, v is the initial velocity, theta is the angle of launch, and g is the acceleration of gravity.

How can you determine the velocity at any point during projectile motion?

The velocity at any point during projectile motion can be determined using the formula: v = v0 + at, where v is the velocity at the desired point, v0 is the initial velocity, a is the acceleration of gravity, and t is the time at the desired point.

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