What is the acceleration along the ground of a 10 kg wagon when its pulled with a force of 44 N at an angle of 35° above the hor
2 answers:
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Answer:
a = 5.05 x 10¹⁴ m/s²
Explanation:
Consider the motion along the horizontal direction
= velocity along the horizontal direction = 3.0 x 10⁶ m/s
t = time of travel
X = horizontal distance traveled = 11 cm = 0.11 m
Time of travel can be given as
inserting the values
t = 0.11/(3.0 x 10⁶)
t = 3.67 x 10⁻⁸ sec
Consider the motion along the vertical direction
Y = vertical distance traveled = 34 cm = 0.34 m
a = acceleration = ?
t = time of travel = 3.67 x 10⁻⁸ sec
= initial velocity along the vertical direction = 0 m/s
Using the kinematics equation
Y = t + (0.5) a t²
0.34 = (0) (3.67 x 10⁻⁸) + (0.5) a (3.67 x 10⁻⁸)²
a = 5.05 x 10¹⁴ m/s²
Answer:
Q should be 4.8 miles east of B.
Explanation:
As the diagram shows, we can simply express the construction cost as a function of angle θ (represented in the diagram).
The length of the pipe in water (represented with blue) = 6/cos θ
The length of the pipe on land (represented with brown) = (8-6*tan θ)
Construction Cost = (6/cos θ) (6000) + (8-6*tan θ)(3750)
The above function represents the construction cost and is in terms of θ
The value of θ varies from 0 degrees to 53.13 degrees as per the diagram.
We can take the derivative of Construction Cost function with respect to θ and equate it to zero to find the angle θ at which the construction cost is minimum.
d(Construction Cost)/d θ = -4500(5*sec θ – 8*tan θ)(sec θ)
-4500(5*sec θ – 8*tan θ) (sec θ) = 0
θ = 38.68 degrees
Using the value of θ, we can find the distance of Q from B.
Distance of Q from B = 6*tan θ
Distance of Q from B = 6*tan (38.68 degrees)
Distance of Q from B = 4.8 miles
