A 13 kg penguin with an initial velocity of 6.0 m/s toward the east runs onto a

Question

A 13 kg penguin with an initial velocity of 6.0 m/s toward the east runs onto a large area of level, frictionless ice. As the penguin slides across the ice, it is pushed by the wind with a force that is constant in magnitude and direction. The figure shows the position of the penguin, at 1.0 s intervals, as it slides on the ice; the positive direction of the x axis is toward the east. The penguin first makes contact with the ice at t = 0. What are the (a) magnitude and (b) direction of the force of the wind on the penguin? Give the direction as a positive (counterclockwise) angle from the +x axis.

A 13 kg penguin with an initial velocity of 6.0 m/s toward the east runs onto a large area of level, frictionless ice. As the penguin slides across the ice, it is pushed by the wind with a force that is constant in magnitude and direction. The figure shows the position of the penguin, at 1.0 s intervals, as it slides on the ice; the positive direction of the x axis is toward the east. The penguin first makes contact with the ice at t0. What are the (a) magnitude and (b) direction of the force of the wind on the penguin? Give the direction as a positive (counterclockwise) angle from the +x axis 10 3s t-2 1= 1 s 10 x (m)

Explanation / Answer

along x axis (east)

during time interval t = 0s to 1 s

displacement x1 = 5m

initial velocity vox = 6 m/s

acceleration ax = ?

x1 = vox*t + (1/2)*ax*t1^2

5 = (6*1) + ((1/2)*ax*1^2)

acceleration ax = -2 m/s^2

force Fx = m*ax = -13*2 = -26 N

along y direction (north)
_________________________

during time interval t = 0s to 1 s

displacement y1 = 0.5 m

initial velocity voy = 0

acceleration ay = ?

y1 = voy*t + (1/2)*ay*t^2

0.5 = 0 +(1/2)*ay*1^2

ay = 1 m/s^2

Fy = m*ay = 13*1 = 13 N

part(a)

magnitude F = sqrt(Fx^2+Fy^2)

F = sqrt(26^2+13^2)

F = 29 N <<<<--------ANSWER

part (b)
____________

direction = tan^-1(Fy/Fx) = +153.4     <<<<--------ANSWER

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