While driving north at 21 m/s during a rainstorm you notice that the rain makes an angle of 36° with the vertical. while drivin
g back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. from these observations, determine the speed and the angle of the raindrops relative to the ground?
1 answer:
Let the velocity of the vehicle be
V₁ = (21, 0)
Let the velocity of a raindrop be
V₂ = (a, b)
When returning, the raindrop is vertical.
Therefore a = 21 m/s
When driving north, a raindrop makes an angle of 36° with the vertical, therefore
tan(36°) = a/b = 21/b
b = 21/tan(36°) = 28.9 m/s
The speed of a raindrop is
√(a² + b²) = √(441 + 835.44) = 35.73 m/s
The angle is 90-36 = 54° with the ground.
Answer: 35.7 m/s at 54° relative to the ground.
V₁ = (21, 0)
Let the velocity of a raindrop be
V₂ = (a, b)
When returning, the raindrop is vertical.
Therefore a = 21 m/s
When driving north, a raindrop makes an angle of 36° with the vertical, therefore
tan(36°) = a/b = 21/b
b = 21/tan(36°) = 28.9 m/s
The speed of a raindrop is
√(a² + b²) = √(441 + 835.44) = 35.73 m/s
The angle is 90-36 = 54° with the ground.
Answer: 35.7 m/s at 54° relative to the ground.
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Answer: An 8 kg book at a height of 3 m has the most gravitational potential energy.
Explanation:
Gravitational potential energy is the product of mass of object, height of object and gravitational field.
So, formula to calculate gravitational potential energy is as follows.
U = mgh
where,
m = mass of object
g = gravitational field =
h = height of object
(A) m = 5 kg and h = 2m
Therefore, its gravitational potential energy is calculated as follows.
(B) m = 8 kg and h = 2 m
Therefore, its gravitational potential energy is calculated as follows.
(C) m = 8 kg and h = 3 m
Therefore, its gravitational potential energy is calculated as follows.
(D) m = 5 kg and h = 3 m
Therefore, its gravitational potential energy is calculated as follows.
Thus, we can conclude that an 8 kg book at a height of 3 m has the most gravitational potential energy.
See this suggested solution.
1. Let a force F' is the vector sum of the forces P and Q, then it is shown on the attached picture and marked with red color.
2. according to the condition the force F holds the object, then F should have the same length as the force F' and the opposite direction.
3. using the conditions described in 2. the answer is C.
