A rescue plane flying horizontally at 72.6 m / s spots a survivor in the ocean 182 m directly below and releases an emergency ki
1 answer:
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Answer:
- k = 167.33 N/m
Explanation:
- The radio waves have a fixed relationship between the propagation speed (the speed of light in vacuum), the frequency and the wavelength, as follows:
- v = c = λ*f
where c= speed of light in vacuum = 3*10⁸ m/s, λ = wavelength =
4.92*10⁷ m.
Solving for f, we get the frequency of the radio waves:
f = 6.1 Hz
- Now, from the Hooke's law, we know that the mass attached at the end of the spring oscillates with an angular frequency defined by a fixed relationship between the spring constant k and the mass m, as follows:
- Now, we know that there exists a fixed relationship between the angular frequency and the frequency, as follows:
- We also know that f in (2) is the same that we got for the radio waves, so replacing (2) in (1), and rearranging terms, we can solve for k, as follows:
a) Vertical velocity: 5.9 m/s
b) Horizontal velocity: 5 m/s
Explanation:
a)
The motion of the ball is the motion of a projectile, which consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction)
- A uniformly accelerated motion (constant acceleration) along the vertical direction
Here we want to find the vertical component of the ball's velocity. This can be done by using the suvat equation for the vertical motion:
where:
is the vertical velocity at time t
is the initial vertical velocity (zero because the ball has been thrown horizontally)
is the acceleration of gravity (here we take downward as positive direction)
Substituting t = 0.6 s, which is the total time of flight, we find the vertical velocity of the ball just before it hits the ground:
b)
The motion along the vertical direction is an accelerated motion, because there is a force (the force of gravity) acting on the ball and that it causes an acceleration in the ball.
However, there are no forces acting in the horizontal direction on the ball (if we neglect the air resistance): this means that the acceleration of the ball in the horizontal direction is zero.
As a consequence, this also means that the horizontal component of the ball's velocity is constant during the motion.
Since the ball was thrown from the table with an initial horizontal velocity of 5 m/s, this means that the horizontal velocity of the ball just before it hits the floor is still