Question

A boat moves through the water with two forces acting on it. One is a 1500 N forward push by the water on the propeller, and the other is an 1300 N resistive force due to the water around the bow.

(a) What is the acceleration of the 1200 kg boat?
(b) If it starts from rest, how far will it move in 7.0 s?
c) What will its velocity be at the end of that time?

Answer 1

0.167 m/s²

4.0915 m

1.169 m/s

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

m = Mass

The resultant force on the boat = 1500-1300 = 200 N

`F=ma\\\Rightarrow a=(F)/(m)\\\Rightarrow a=(200)/(1200)\\\Rightarrow a=0.167\ m/s^2`

Acceleration of the boat is 0.167 m/s²

`s=ut+(1)/(2)at^2\\\Rightarrow s=0* 7+(1)/(2)* 0.167* 7^2\\\Rightarrow s=4.0915\ m`

The boat will travel 4.0915 m in 7 seconds

`v^2-u^2=2as\\\Rightarrow v=√(2as+u^2)\\\Rightarrow v=√(2* 0.167* 4.0915+0^2)\\\Rightarrow v=1.169\ m/s`

The velocity of the boat at the end of 7 s is 1.169 m/s