A cruise ship of seniors is moving due west with an engine speed of 60km/hr when it encounters a current from the North at 20Km/hr. What is its relative velocity due to this current? (speed and angle) What course correction does it need to continue due west? (new angle and resulting speed)
To find the relative velocity due to the current, we need to use vector addition. The cruise ship's velocity due west is its engine speed of 60 km/hr. The current's velocity is toward the north at 20 km/hr. Since these velocities are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resulting velocity.
The magnitude of the resulting velocity can be calculated using the formula:
resultant velocity = √(velocity of ship^2 + velocity of current^2)
resultant velocity = √(60^2 + 20^2)
resultant velocity = √(3600 + 400)
resultant velocity = √4000
resultant velocity ≈ 63.246 km/hr
Now, to find the angle, we can use trigonometry. Since we have a right-angled triangle formed by the ship's velocity due west and the current's velocity, we can use the inverse tangent function (tan^(-1)) to find the angle.
angle = tan^(-1)(velocity of current / velocity of ship)
angle = tan^(-1)(20 / 60)
angle = tan^(-1)(1/3)
angle ≈ 18.435 degrees
Therefore, the relative velocity of the cruise ship due to the current is approximately 63.246 km/hr at an angle of approximately 18.435 degrees north of due west.
To continue due west, the cruise ship needs to correct its course to counteract the effect of the current. The new angle would be exactly opposite to the angle calculated earlier, which is 18.435 degrees south of due west. The resulting speed would be the same as the ship's original speed due west, which is 60 km/hr.