A turtle ambles leisurely-as turtles tend to do-when it moves from a location wi

Question

A turtle ambles leisurely-as turtles tend to do-when it moves from a location with position vector r_1,x = 1.79m and r_2,y = -2.21m in a lettuce garden to another location, with position vector r_2,x = 3.23 meter and r_2,y = -4.01 meter, where the lettuce appears to be tastier (but really isn't-this turtle can't see too well). The excursion takes 3.50*10^2 seconds to complete. What are the components and the magnitude of the turtle's average velocity, in meters per second? v_av,x = v_av,y = |v vector_av| =

Explanation / Answer

The velocity of a body without acceleration can be determined with the relationship

V = Deltd/ Delt t      Delt symbol for variation of the magnitud

As in this case we have the x axis displacement components, and we calculate speeds in each axis separately, remember that time is a scalar which the same for everyone.

Part A     Axis X

. r1x = 1.79 m

. r2x = 3.23 m

. t = 3.50 102 s       this is the variation (tf-ti)

Vx = (r2x – r1x)/ (tf-ti)

Vx = 3.23-1.79/ ( 3.50 102)

Vx = 1.44/ 3.50 102

Vx= 41.1 m/s

Part B      Axis Y

. r1y = -2.21 m

. r2y =-4.01 m

Vy = (r2y – r1y)/ (tf-ti)

Vy= (-4.01 + 2.21) / 3.50 102

Vy= - 1.8/ 3.50 102

Vy = -51.4 m/s

Part C      find the module and angle of this speed

Using trigonometry and the Pythagorean triangle

V2 = Vx2 + Vy2         

V2 = 41.12+ (-51.4)2                    V2   =4331.17      V= sqrt(V2)

V = 65.8 m/s

Tg anlge = Vy/Vx      Tg angle = -51.4/41.1       tg angle = -1.25

. angle = -51.4°

This angle is measured clockwise under the x-axis  

The measure in an anti-clockwise direction is 360-51.4 = 308. 6|   This is measured from the positive side of the x-axis

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