Answer:
The period of a wave is the duration it takes to complete one full oscillation, such as from one peak to the next trough.
Since the period is expressed in microseconds, it needs to be converted into seconds.
The conversion is:
Accordingly, the wave's period in seconds is .
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!
The speed resulting from the plane is (3) 226 m/s
Reasoning:
We can determine the plane's resultant speed using the Pythagorean Theorem because the two speeds form a right angle (creating a right triangle).
Thus, the computation is as follows:
Consequently, the plane's resultant speed is (3) 226 m/s
Have a wonderful day!