The accurate answer is 36 miles per hour
Explanation:
To calculate the average speed, start by determining the total distance and total time Lucy traveled, as average speed is the total distance divided by the total time.
Total Distance
Lucy is known to have covered 2/3 of the total distance initially, later finishing the journey with 60 miles. Therefore, the last segment of 60 miles corresponds to 1/3 of the total distance.
(Total distance)
Consequently, since 60 miles equals one-third, multiplying this by 3 gives the total distance: 180 miles.
This indicates the total distance traversed is 180 miles
Total Time
Lucy took 3 hours for the first part of her journey and 2 hours for the second, leading to a total time of 5 hours (3 + 2 = 5)
Determining Average Speed
Thrust is quantified as a reaction force, in accordance with Newton's third law. When a system accelerates or expels mass in one direction, this resulting mass generates a force of equal strength but in the opposite direction on that system. This relationship can be expressed mathematically as:
Where:
v = velocity of the exhaust gases as perceived from the rocket.
= Change in mass over time
The provided data is as follows:
After substitution, we obtain:
Answer:
The BMX rider lands 5.4 meters horizontally away from the ramp's end.
Explanation:
The BMX position vector is represented as:
r = (x0 + v0 × t × cos α, y0 + v0 × t × sin α + ½ × g × t²)
Where:
r = position at time t
x0 = initial horizontal position
v0 = initial speed
α = angle of jump
y0 = initial vertical height
g = gravitational acceleration (-9.8 m/s², upward positive)
Refer to the diagram for clarity. At the landing time, the vertical coordinate of the position vector is -2.4 m, measured from the ramp's edge as the origin. Using the vertical component equation for y, one can solve for t, then substitute t to find the horizontal distance.
The vertical position equation:
-2.4 m = 0 + 5.9 m/s × t × sin 40° - ½ × 9.8 m/s² × t²
Rearranged:
0 = -4.9 t² + 5.9 t × sin 40° + 2.4
Solving this quadratic yields:
t = 1.2 seconds
Then, calculate horizontal distance:
x = 0 + 5.9 m/s × 1.2 s × cos 40° = 5.4 m
This means the BMX lands 5.4 meters from the ramp's edge.
Have a great day!
Answer:
the time it takes after impact for the puck is 2.18 seconds
Explanation:
initially given information
mass = 30 g = 0.03 kg
diameter = 100 mm = 0.1 m
thickness = 0.1 mm = 1 × m
dynamic viscosity = 1.75 × Ns/m²
temperature of air = 15°C
to determine
time needed for the puck to reduce its speed by 10%
solution
we note that velocity changes from 0 to v
assuming initial velocity = v
therefore final velocity = 0.9v
implying a change in velocity is du = v
and clearance dy = h
shear stress acting on the surface is expressed as
= µ
therefore
= µ ............1
substituting the values
= 1.75 × ×
= 0.175 v
the area between the air and puck is given by
Area =
area =
area = 7.85 × m²
thus, the force on the puck can be represented as
Force = × area
force = 0.175 v × 7.85 ×
force = 1.374 × v
now applying Newton's second law
force = mass × acceleration
- force =
- 1.374 × v =
solving for t =
the time needed after impact for the puck is 2.18 seconds