What is the acceleration of all objects due to gravity? What does this mean?

Answer:

To solve this problem, we can use the kinematic equation for horizontal motion, which relates the initial velocity ($v_{0}$), final velocity ($v_{f}$), acceleration ($a$), and displacement ($d$) of an object:

$d = v_{0} t + \frac{1}{2}at^{2}$

In this case, we want to find the minimum initial velocity ($v_{0}$) that the divers must have to clear the rock. To do this, we can assume that the divers just graze the rock at the start of their trajectory, so the displacement in the horizontal direction is equal to the distance from the cliff to the rock ($d = 9.34 m$). We also know that the acceleration in the horizontal direction is zero, so the only force acting on the divers is gravity in the vertical direction, which gives an acceleration of $a = 9.8 m/s^{2}$.

At the instant the divers leave the cliff, they have zero horizontal velocity, so $v_{0} = 0$. We can use the equation above to solve for the time it takes for the divers to fall from the cliff to the level of the rock:

$d = \frac{1}{2}at^{2} \Rightarrow t = \sqrt{\frac{2d}{a}}$

Plugging in the numbers, we get:

$t = \sqrt{\frac{2(9.34 m)}{9.8 m/s^{2}}} \approx 1.44 s$

Since the cliff divers want to clear the rock, they need to travel a horizontal distance of at least $9.34 m$ during this time. We can use the equation for horizontal motion again to solve for the minimum initial velocity:

$d = v_{0}t \Rightarrow v_{0} = \frac{d}{t} = \frac{9.34 m}{1.44 s} \approx 6.49 m/s$

Therefore, the minimum horizontal velocity that the cliff divers must have to clear the rock is approximately $6.49 m/s$.

The wavelength of the sound emitted is 3.33 x 10⁵ m.

What is wavelength?

The wavelength is the distance between the adjacent crest or trough of the sinusoidal wave. The wavelength is the reciprocal of the frequency of the wave.

Wavelength λ = 1/f

If a dog whistle has a frequency of 30000 Hz, then the wavelength will be

λ = 1/f

λ = 1/30000

λ = 3.33 x 10⁵ m

Thus, the wavelength of the sound of dog emitted is 3.33 x 10⁵ m

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A) 30 m/s

The problem can be solved by using the law of conservation of momentum. In fact, the total momentum falcon+pigeon before the collision must be equal to the total momentum falcon+pigeon after the collision:

where

mf = 0.480 g is the mass of the falcon

uf = 45 m/s is the initial velocity of the falcon

mp = 0.240 g is the mass of the pigeon

up = 0 is the initial velocity of the pigeon

v is the final combined velocity of pigeon+falcon

Solving the equation for v, we find

B) 480 N

The average force on the pigeon during the impact is given by

where

is the change in momentum of the pigeon

is the duration of the collision

here we have:

- Change in momentum of the pigeon:

- Duration of the collision:

So the average force is

Final answer:

To determine the final speed of the falcon and pigeon, we need to use the principles of conservation of momentum. To calculate the average force on the pigeon during the impact, we can use the equation for impulse. The primary topic of this question is conservation of momentum and impulse.

Explanation:

To determine the final speed of the falcon and pigeon, we need to use the principles of conservation of momentum. Since the pigeon is assumed to be stationary, its initial momentum is zero. The final momentum of the falcon and pigeon combined must also be zero, according to the law of conservation of momentum. Using the equations for momentum and rearranging, we can solve for the final speed of both the falcon and pigeon.

To calculate the average force on the pigeon during the impact, we can use the equation for impulse, which is the change in momentum. Impulse is equal to force multiplied by the time of impact. Rearranging the equation, we can solve for force.

Learn more about Conservation of Momentum and Impulse here:

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