A boat with a mass of 1 t floats under the action of three forces, the engine thrust force of 1.5 kN, the wind force of 1 kN, and the resistance force of 0.5 kN, and the thrust force and wind force are perpendicular to each other. what is the acceleration of the boat?
m = 1 t = 1000 kg.
Fdv = 1.5 kN = 1500 N.
Fvet = 1 kN = 1000 N.
Fcopr = 0.5 kN = 500 N.
Let us find the power module of the boat F, if there were no movement resistance force. Since the power of the boat engine Feng and the wind force Fvet are directed perpendicular to each other, their resulting force F will be the hypotenuse of a right-angled triangle with legs Feng and Fvet.
By the Pythagorean theorem, F = √ (Fdv ^ 2 + Fvet ^ 2).
F = √ ((1500 N) ^ 2 + (1000 N) ^ 2) = 1802.7 N.
Since the resistance force is always directed against the movement, the resulting force Fres of all three forces (Fdw, Fvet, Fsopr) will be determined by the formula: Fres = F – Fsopr.
Fres = 1802.7 N – 500 N = 1302.7 N.
For the resulting force, we write 2 Newton’s law: Fres = m * a.
a = Fres / m.
a = 1302.7 N / 1000 kg = 1.3 m / s ^ 2.
Answer: the acceleration of the boat relative to the coast a = 1.3 m / s ^ 2.
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