Answer:
The magnitude and direction of its acceleration is 1.284 m/s² North-East
Explanation:
Given;
The force exerted by the wind on the sails of a sailboat to be 360 N north
The force exerted by water on the sails of a sailboat to be 170 N east.
The resultant force on the boat is can be calculated by Pythagoras theorem, if these two forces makes right angled-triangle.
R² = N² + E²
R² = (360)² + (170)²
R² = 158500
R = √(158500)
R = 398.121 N
If the If the boat (including its crew) has a mass of 310 kg, then the magnitude and direction of its acceleration becomes;
a = F/m
a = 398.121/310
a = 1.284 m/s² North-East
Answer:
Explanation:
The North and East forces are 90° apart, making a right triangle with the resultant as the hypotenuse. Using trigonometry equations,
(170)² + (360)² = F²
28900 + 129600 = F²
√(158500) = F
398.12 N = F
Remember,
F = ma
398.12 N = (310 kg) × a
398.12/310kg = a
1.28 m/s² = a
The sailboat will be heading North East. The angle of the boats trajectory use inverse tangent function.
tan(Ф) = opposite/adjacent
= arctan(opposite/adjacent)
= arctan(360/170)
= 64.7° North East.
