Question

A boat leaves the dock at t = 0 and heads out into a lake with an acceleration of 2.0m/s²ˆi. A strong wind is pushing the boat, giving it an additional velocity of 2.0m/sˆi+1.0m/sˆj. (a) What is the velocity of the boat at t = 10 s? (b) What is the position of the boat at t = 10s? Draw a sketch of the boat’s trajectory and position at t = 10 s, showing the x- and y-axes.

a) (i) 20.0i+10.0j m/s
(ii) 12.0i+10.0j m/s
(iii) 22.0i+10.0j m/s
(iv) 24.0i+12.0j m/s

b) (i) 110.0i+10.0j m
(ii) 120.0i+10.0j m
(iii) 100.0i+10.0j m
(iv) 130.0i+10.0j m

Answer 1

The velocity of the boat at t = 10s is 22.0i+10.0j m/s and the position of the boat at t = 10s is 120.0i+10.0j m.

Step-by-step explanation:

To find the velocity of the boat at t = 10s, we need to calculate the net velocity by adding the boat's acceleration and the wind's velocity together.

The boat's acceleration is given as 2.0 m/s²î and the wind's velocity is given as 2.0 m/sî + 1.0 m/sĵ.

So, the net velocity of the boat at t = 10s is (2.0 m/s²î)(10s) + (2.0 m/sî + 1.0 m/sĵ) = 20.0 m/sî + 10.0 m/sĵ.

To find the position of the boat at t = 10s, we can use the formula for displacement.

The boat's initial position is 0, and the velocity at t = 10s is 20.0 m/sî + 10.0 m/sĵ.

So, the position of the boat at t = 10s is (20.0 m/sî + 10.0 m/sĵ)(10s) = 200.0 mî + 100.0 mĵ.

Therefore, the correct answers are (iii) 22.0i+10.0j m/s and (ii) 120.0i+10.0j m.