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godtripp said:Hmmm, since it doesn't say anything about the boy's direction when he starts swimming I assume they want you to consider a right triangle...of course this depends on your level of physics class also... if you find this is not the case then use the law of cosines to solve the problem .
Consider a right triangle with edge AB as the bank shore. edge AC as the path of the boat and edge BC as the path the boy swims to reach the boat
angle ABC = 90 deg
and angle BAC = 15 deg
now the problem becomes easy if you think of these edges as vectors So edge AC is the vector representing the boat's velocity. The edges CB and AB represent components of the boys velocity
then find the magnitude of the boy's velocity by sqrt ( CB^2 + AB^2 ) and violla ... v(max) = sqrt(20)
again... this is assuming the boys swims perpendicular to the shore.. if you're in a college course with a calculus prerequisite ... you might want to introduce some variable angle theta for angle ABC and do some calculus to find out which angle would give you a minimum time. (related rates) and then solve for the vector sum that way
godtripp said:Consider a right triangle with edge AB as the bank shore. edge AC as the path of the boat and edge BC as the path the boy swims to reach the boat
angle ABC = 90 deg
and angle BAC = 15 deg
now the problem becomes easy if you think of these edges as vectors So edge AC is the vector representing the boat's velocity. The edges CB and AB represent components of the boys velocity
then find the magnitude of the boy's velocity by sqrt ( CB^2 + AB^2 ) and violla ... v(max) = sqrt(20)
Relative velocity is the velocity of an object in relation to another object. It takes into account the motion of both objects and is measured in terms of distance traveled per unit of time.
Relative velocity is calculated by subtracting the velocity of one object from the velocity of the other object. This gives the relative velocity between the two objects.
The relative velocity between the boy and the ship will determine whether or not the boy is able to catch the ship. If the boy's relative velocity is greater than the ship's, he will be able to catch it. If the ship's relative velocity is greater, the boy will not be able to catch it.
Yes, relative velocity can change depending on the motion of the objects. If either object changes its velocity, the relative velocity between them will also change.
Direction plays a crucial role in calculating relative velocity. If both objects are moving in the same direction, their relative velocity will be different than if they are moving in opposite directions. This is because the direction of motion affects the overall velocity of the objects.