Daring Darless wishes to cross the Grand Canyon of the Snake River by being shot from a cannon. She wishes to be launched at 65

Answer:

17.35 × 10^(-6) m

Explanation:

Mass; m = 50 kg

Weight; W = 554 N

From the formula:

W = mg

This simplifies to; 554 = 50g

g = 554/50

g = 11.08 m/s²

Also, using the formula;

mg = GMm/r²

hence; g = GM/r²

Rearranging gives;

r = √(GM/g)

With G as a known constant of 6.67 × 10^(-11) Nm²/kg²

r = √(6.67 × 10^(-11) × 50/11.08)

r = 17.35 × 10^(-6) m

Answer:

Height (h) = 17 m

Velocity (v) = 18.6 m/s

Explanation: This problem can be solved using kinematic motion equations.

Given Data

Initial velocity (u) = 0

Acceleration (a) = g

Time (t) = 1.9 seconds

First, we calculate the height.

Then, we find the final velocity

The acceleration graph is a linear representation described by y=9.8, as it remains constant:

The velocity graph can be represented by y=9.8x (where y signifies velocity and x indicates time):

The displacement graph can be described as y=4.9x^2 (with x as time and y as displacement):

These graphs apply exclusively from x=0 to x=1.9, so disregard other sections of the graphs.

Answer:

The beats frequency measures approximately

4.4 kHz

Explanation:

The beat frequency arises from the original ultrasound frequency, , and the frequency of the sound reflected off the car, :

(1)

To calculate the frequency of the reflected sound, we apply the Doppler effect formula:

where

v = 340 m/s, the speed of sound

is the velocity of the car

is the frequency of the sound emitted

By substituting values,

Thus, the beat frequency (1) is

<span>A centripetal force maintains an object's circular motion. When the ball is at the highest point, we can assume that the ball's speed v is such that the weight of the ball matches the required centripetal force to keep it moving in a circle. Hence, the string will not become slack. centripetal force = weight of the ball m v^2 / r = m g v^2 / r = g v^2 = g r v = sqrt { g r } v = sqrt { (9.80~m/s^2) (0.7 m) } v = 2.62 m/s Thus, the minimum speed for the ball at the top position is 2.62 m/s.</span>

Answer:

The separation between Earth and the star is growing.

Explanation:

When we witness the electromagnetic radiation of an object shifting towards the blue spectrum, it indicates that the object is moving closer, which compresses the light waves and decreases the wavelength towards blue, referred to as blueshift.

Conversely, when an object retreats from us rapidly, its light waves are stretched, resulting in a longer wavelength that shifts towards the red part of the spectrum. This shift is termed redshift.

The alteration of wavelength and frequency due to relative motion (approaching or receding) is explained by the Doppler effect.

In this case, since the light we detect from the star has transitioned to the red part of the spectrum, we can infer that it is moving away from Earth, indicating that the distance between the star and Earth is increasing.