A car travels 5 km due east, then 10 km due north, and then 5
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Answer:
The distance from the base of the building to the landing site is 154 m.
The total flight time is 3.5 s.
At the moment of impact, the velocity vector of the cat is v = (44 m/s, -34.3 m/s) and its magnitude is 55.8 m/s.
Explanation:
The equations for the position and velocity vectors of the cat are as follows:
r = (x0 + v0x · t, y0 + v0y · t + 1/2 · g · t²)
v = (v0x, v0y + g · t)
Where:
r = position vector of the cat at time t.
x0 = initial horizontal position.
v0x = initial horizontal velocity.
t = time.
y0 = initial vertical position.
v0y = initial vertical velocity
g = acceleration due to gravity (-9.8 m/s² considering the upward position as positive).
v = velocity vector of the cat at time t.
Please, see the attached figure for a better understanding of the problem. Notice that the origin of the frame of reference is located at the launching point so that x0 and y0 = 0. In a horizontal launch, initially there is no vertical velocity, then, v0y = 0.
When the cat reaches the ground, the position vector of the cat will be r1 (see figure). The vertical component of r1 is -60 m and the horizontal component will be the horizontal distance traveled by the cat (r1x). Then, using the equation of the y-component of the position vector, we can obtain the time of flight and with that time we can obtain the horizontal distance traveled by the cat:
r1y = y0 + v0y · t + 1/2 · g · t²
-60 m = 0 m + 0 m/s · t - 1/2 · 9.8 m/s² · t²
- 60 m = -4.9 m/s² · t²
-60 m / - 4.9 m/s² = t²
t = 3.5 s
The cat reaches the ground in 3.5 s
Now, we can calculate the horizontal component of r1:
r1x = x0 + v0 · t
r1x = 0 m + 44 m/s · 3.5 s
r1x = 154 m
The distance from the base of the building to the landing site is 154 m.
The total flight time was already calculated and is 3.5 s.
The velocity vector of the cat when it reaches the ground will be:
v = (v0x, v0y + g · t)
v = (44 m/s, 0 m/s - 9.8 m/s² · 3.5 s)
v = (44 m/s, -34.3 m/s)
The magintude of the vector "v" is calculated as follows:
At the moment of impact, the velocity vector of the cat is v = (44 m/s, -34.3 m/s) and its magnitude is 55.8 m/s.
Answer:
The force is
Explanation:
The diagram for this question is shown on the first uploaded image
At Equilibrium the summation of the of force on the vertical axis is zero
i.e
=>
is the is the speed of water at the nozzle which can be mathematically evaluated as
substituting for R and
for
is the is the speed of water at the pipe which can be mathematically evaluated as
substituting for R and
for
is he density of water with value
Substituting values into the equation above
At Equilibrium the summation of the of force on the horizontal axis is zero
i.e
=>
Since The speed at both A and B nozzle are the same then remains the same
Substituting values
=>
Hence the force acting on the flange bolts required to hold the nozzle in place is
