A boat moving at 7.8 km/hr relative to the water is crossing a river 3.5 km wide in which the current is flowing at 2.8 km/hr. A
t what angle upstream should the boat head to reach a point on the other shore directly opposite the starting point?
1 answer:
Answer:
Explanation:
Given
velocity of boat with respect to river
velocity of river is
River is 3.5 km wide
Suppose boat leaves at an angle of with vertical such that it reaches exactly opposite end of initial Point
Therefore
component will balance the river Flowso that sin component helps to cross the river
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a) The momentum of the coconut is 3 kg m/s
b) At first, the air resistance is negligible, so the coconut accelerates due to the force of gravity
c) The coconut reaches its terminal velocity
Explanation:
a)
The momentum of an object is given by the equation
where
m is the mass of the object
v is its velocity
For the coconut in this problem, we have:
m = 1.5 kg (mass)
v = 2 m/s (velocity)
Therefore, its momentum is
B)
There are only two forces acting on the coconut during its fall:
- The force of gravity, of magnitude
(m= mass of the coconut, g = acceleration of gravity), acting downward
- The air resistance, acting upward, whose magnitude is proportional to the speed of the coconut
During the first momentums of the fall, the speed of the coconut is still low, so the air resistance is mostly negligible, and therefore only the force of gravity is acting on the coconut. Since this force is constant, it means that the acceleration of the coconut is constant: therefore, its velocity keeps increasing during the fall, and the coconut speeds up.
C)
If the tree is very tall, the fall of the coconut lasts long, and the speed of the coconut keeps increasing. Since the air resistance is proportional to the speed, this means that at some point, the air resistance is no longer negligible, and it starts to have some effect on the fall of the coconut. In particular, at a certain point, the air resistance will become equal (in magnitude) to the force of gravity (but opposite in direction): this means that from this point, the acceleration of the coconut will be zero, and therefore the coconut will continue its motion at constant velocity. This velocity is called terminal velocity, and it occurs when the force of gravity is equal to the air resistance:
where is the air resistance.
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Answer:
Explanation:
The density of a material is given by:
(1)
Where:
is the mass of the cube
is the volume of the cube
Now, the volume of a cube is equal to the length of its edge to the power of 3:
(2)
If we know , the volume of this cube is:
(3)
Substituting (3) in (1):
(4)
This is the density of the cube