Show your work: 1.) A dog runs toward an anthropomorphic fire hydrant with a con

Question

Show your work:

1.) A dog runs toward an anthropomorphic fire hydrant with a constant speed of 5 m/s. When it is 20 m away, the fire hydrant itself runs away from rest with an acceleration of 0.3 m/s2. How far does the hydrant run before it is caught?

a) 3.2 m b) 6.4 m c) 9 m d) 1.8 m e) none

2.) An object has an equation of mostion as follows: r(t) = (6t2 - 5t)x - (2t3 - 18)y. What angle does its velocity make with the x-axis at 14 sec?

a) 45 degrees b) -82 degrees c) -111 degrees d) 78 degrees e) none

3) A rugby player runs with the ball directly towards the goal along +x-axis. He has a speed relative to the ground of 4 m/s. His pass has a speed of 7.5 m/s relative to him. What is the smallest angle relative to the +x-axis for his pass to be legal (backwards relative to field).

a) 90 degrees b) 82 degrees c) 122.2 degrees c) 145.1 d) 0 degrees e) none

a) d/t b) 0 c) 2d/3t d) 4d/3t e) none

Explanation / Answer

1. given

v = 5 m/s

d = 20 m

a = 0.3 m/s/s , 0 initial speed

let the hydrant tun for x distance before getting caught

then

vt - x = d

x = 0.5*at^2

hence

5t - 0.15t^2 = 20

solving

0.15t^2 - 5t + 20 = 0

t^2 - 33.33t + 133.33 = 0

t = 4.648 s

hence

x = 3.241517691 m

option a

2. r = (6t^2 - 5t)x - (2t^3 -18)y

at t = 14 s

t' = (12t - 5)x - (6t^2)y

theta = arctan(-6t^2/(12t - 5)) = -82.1087 dqg below x axis

3. v = 4m/s

vp = 7.5 m/s

relative to x axis, the smallesrt angle for which his pass is legal is phi

then

vp*cos(phi) = v

phi = 122.23 deg

option c)

4. width = d

time = t

walks back the same distance in time 2t

avg speed = 2d/3t

absolute average velocity = 0

hence

difference = 2d/3t

option c)

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