18)An airplane has to fly eastward to a destination 856 km away. If wind is blowing at 18.0 m/s northward and the air speed of the plane is 161 m/s, in what direction should the plane head to reach its destination?
6.42 degrees south of east
19)A 4400 kg can accelerate from 0-25m/s in 4 seconds. What force must the engine create to accomplish this acceleration?
I don't know
20)An elevator is moving up with an acceleration of 3.36 m/s^2. What would be the apparent weight of a 64.2 kg man in the elevator?
I don't know
8)An airplane has to fly eastward to a destination 856 km away. If wind is blowing at 18.0 m/s northward and the air speed of the plane is 161 m/s, in what direction should the plane head to reach its destination?
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The 856 km has nothing to do with it. The point is - fly east.
North components come out to zero
18 - 161 sin(angle south of east) = 0
sin angle = .112
angle = 6.42 check
6.42 degrees south of east
19)A 4400 kg can accelerate from 0-25m/s in 4 seconds. What force must the engine create to accomplish this acceleration?
I don't know
==
F = m a
a = 25/m/s / 4 s = 6.25 m/s^2
F = 4400 * 6.25
20)An elevator is moving up with an acceleration of 3.36 m/s^2. What would be the apparent weight of a 64.2 kg man in the elevator?
I don't know
=
F = ma
Force up from elevator on man - weight of man = mass * a
F - m (9.8) = m (3.36)
F = 64.2 * (13.2)
ok I got 847.44 for #20 but that's not one of my choices. they are: 215.71, 413.45, 844.87, and need more info
I agree with you, 847 N
18) To determine the direction the plane should head, we need to consider the effect of the wind on the plane's actual velocity. This can be done using vector addition.
Step 1: Determine the components of the wind and plane velocities.
Given data:
Wind speed: 18.0 m/s (northward)
Plane speed: 161 m/s (eastward)
Step 2: Express the wind and plane velocities as vectors.
Wind velocity: v_wind = 18.0 m/s (northward)
Plane velocity: v_plane = 161 m/s (eastward)
Step 3: Calculate the resultant velocity.
The resultant velocity is the sum of the wind and plane velocities.
v_resultant = v_wind + v_plane
Step 4: Determine the magnitude and direction of the resultant velocity.
To find the magnitude and direction of the resultant velocity, we can use the Pythagorean theorem and trigonometry.
Magnitude: |v_resultant| = sqrt((v_resultant_x)^2 + (v_resultant_y)^2)
Direction: θ = arctan(v_resultant_y / v_resultant_x)
In this case:
v_resultant_x = v_plane = 161 m/s (eastward)
v_resultant_y = v_wind = 18.0 m/s (northward)
Therefore:
|v_resultant| = sqrt((161)^2 + (18.0)^2) ≈ 161.34 m/s
θ = arctan(18.0 / 161) ≈ 6.42 degrees
So, the plane should head approximately 6.42 degrees south of east to reach its destination.
19) To find the force required to accomplish the acceleration, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
Given data:
Mass of the object (can): 4400 kg
Acceleration: 25 m/s^2
Force = Mass × Acceleration
F = 4400 kg × 25 m/s^2
F = 110000 N
Therefore, the engine must create a force of 110000 Newtons to accomplish this acceleration.
20) To find the apparent weight of the man in the elevator, we need to consider the acceleration of the elevator.
Given data:
Mass of the man: 64.2 kg
Acceleration of the elevator: 3.36 m/s^2
Step 1: Calculate the force acting on the man.
Force = Mass × Acceleration
F = 64.2 kg × 3.36 m/s^2
F ≈ 215.712 N
Step 2: Calculate the apparent weight.
The apparent weight is the force acting on the man due to the acceleration of the elevator. It is the difference between the actual weight and the force due to the acceleration.
Apparent weight = Actual weight - Force due to acceleration
Apparent weight = Mass × Gravity - Force
In this case:
Gravity (g) ≈ 9.8 m/s^2 (acceleration due to gravity)
Apparent weight = (64.2 kg × 9.8 m/s^2) - 215.712 N
Apparent weight ≈ 628.548 N
Therefore, the apparent weight of the man in the elevator would be approximately 628.548 Newtons.