Forces 2 dimensions: How far have the tugboats moved the log

[Evangeline101]

Homework Statement

Two tugboats are pulling on a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s?

Homework Equations

c² = a² + b² - 2abcosC

c = (a² + b²- 2abcosC)^1/2

The Attempt at a Solution

[/B]
c² = a² + b² - 2abcosC

c = (a² + b²- 2abcosC)^1/2

c = [(400 N)² + (800 N)² - 2 (400 N) x (800 N) cos 150°]^1/2

c= 1164 N

sinβ/800 N = sin 150°/ 1164 N

β = 20°

(To determine the angle for F_net, subtract 10° from 20°, which equals 10°, as this results in the angle needed to describe the direction for F_net.)

Fnet = 1164 N [W 10° N]

a = 1164 N [W 10° N] / 250 kg

= 4.66 m/s² [W 10° N]

Δd = ½ 4.66 m/s²[W 10° N] x (10 s)²

Δd = 233 m [W 10° N]

The tugboats have moved the log 233 m [W 10° N] after 10 seconds.

Is this correct?

 

[haruspex]

Homework Statement

Two tugboats are pulling on a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s?
View attachment 100372

Homework Equations

c² = a² + b² - 2abcosC

c = (a² + b²- 2abcosC)^1/2

View attachment 100373

The Attempt at a Solution

[/B]
c² = a² + b² - 2abcosC

c = (a² + b²- 2abcosC)^1/2

c = [(400 N)² + (800 N)² - 2 (400 N) x (800 N) cos 150°]^1/2

c= 1164 N

sinβ/800 N = sin 150°/ 1164 N

β = 20°

(To determine the angle for F_net, subtract 10° from 20°, which equals 10°, as this results in the angle needed to describe the direction for F_net.)

Fnet = 1164 N [W 10° N]

a = 1164 N [W 10° N] / 250 kg

= 4.66 m/s² [W 10° N]

Δd = ½ 4.66 m/s²[W 10° N] x (10 s)²

Δd = 233 m [W 10° N]

The tugboats have moved the log 233 m [W 10° N] after 10 seconds.

Is this correct?

Looks good.

 

[Evangeline101]

Ok thanks :)