A speed boat is moving across the surface of a lake. At t_1=0 with the component

Question

A speed boat is moving across the surface of a lake. At t_1=0 with the components of its velocity are V_x= 25 m/s and V_y= -10 m/s. At T_2=15s the components are V_x= 12 m/s and V_y= -21 m/s.
a) what was the change in magnitude and direction of the boat's velocity during this time? b) what are the components of the average acceleration for the interval? c) what are the magnitude and direction of the average acceleration for this interval? A speed boat is moving across the surface of a lake. At t_1=0 with the components of its velocity are V_x= 25 m/s and V_y= -10 m/s. At T_2=15s the components are V_x= 12 m/s and V_y= -21 m/s.
a) what was the change in magnitude and direction of the boat's velocity during this time? b) what are the components of the average acceleration for the interval? c) what are the magnitude and direction of the average acceleration for this interval?
a) what was the change in magnitude and direction of the boat's velocity during this time? b) what are the components of the average acceleration for the interval? c) what are the magnitude and direction of the average acceleration for this interval?

Explanation / Answer

a) dvx = 12-25 = -13

dvy = -21 - (-10) = -11

mag = sqrt(13^2 + 11^2)= 17.03 m/s

direction = arctan(y/x) = arctan(11/13)= 220.24 degrees

b)

ax = dvx/dt = -13/15

ay = dvy/dt = -11/15

c) mag = 17.03/15= 1.14 m/s^2

direction = 220.24 degrees

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