While visiting Planet Physics, you toss a rock straight up at 15 m/s and catch it 2.4 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 240 min.

What is the mass of Planet Physics?

What is the radius of Planet Physics?

15 m/s and catch it 2.4 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 240 min.

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t up = 1.2s
a = -gphysics
v = 15 - g t
0 = 15 - gphysics (1.2)
g physics = 15/1.2
gphysics = 12.5 m/s^2

on surface
F = m gphysics = G m Mphysics/Rphysics^2
so
12.5 = G Mphysics/Rphysics^2

in orbit
F = G mship Mphysics/4Rphysics^2 = mship v^2/2 Rphysics

12.5 = 2v^2 /( Rphysics)

T = 240*60 = 2 pi (2Rphysics)/v
so
v^2 = [4 pi Rphysics/(240*60)]^2
so
12.5 = 2[4 pi Rphysics/(240*60)]^2/Rphysics

solve for Rphysics and go back for Mphysics

0976151624

To find the mass of Planet Physics, we can use the formula for gravitational force:

F = G * (m1 * m2) / r^2,

where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.

In this case, we can consider the rock as m1 and Planet Physics as m2. The only information given about the rock is its initial velocity, but we need more information to find its mass. So, we will not be able to determine the mass of Planet Physics with the given information.

Similarly, the information provided does not allow us to directly determine the radius of Planet Physics. We only know that the cruise ship orbits at an altitude equal to the planet's radius every 240 minutes. However, without knowing any other information about the cruise ship or its orbit, we cannot determine the radius of Planet Physics.

To find the mass of Planet Physics, we need to use the information provided about the rock toss and the cruise ship's orbit.

First, let's consider the rock toss. We know that the initial velocity of the rock, when tossed straight up, is 15 m/s. We also know that it takes 2.4 seconds for the rock to reach its highest point and come back down to be caught.

When the rock reaches its highest point, its velocity will be zero before it starts coming back down. This means that the time it takes to reach the highest point is half of the total time of 2.4 seconds.

So, the time it takes for the rock to reach its highest point is 2.4 seconds / 2 = 1.2 seconds.

To calculate the maximum height the rock reaches, we can use the following equation from kinematics:

v² = u² + 2as

Where:
v = final velocity (zero at the highest point)
u = initial velocity (15 m/s)
a = acceleration (due to gravity, approximately -9.8 m/s²)
s = distance or displacement

Rearranging the equation to solve for s:

s = (v² - u²) / (2a)

Plugging in the values, we have:

s = (0 - (15)²) / (2 * -9.8) = -225 / -19.6 = 11.48 meters (rounded to two decimal places)

The maximum height the rock reaches is approximately 11.48 meters.

Now, let's consider the orbit of the cruise ship. We know that the cruise ship orbits at an altitude equal to the planet's radius every 240 minutes.

The time it takes for an object to complete one full orbit is known as the orbital period. In this case, the orbital period is 240 minutes.

The formula to calculate the orbital period of an object in circular motion is:

T = 2π√(r³/GM)

Where:
T = orbital period
π = pi (approximately 3.14159)
r = radius of orbit (equal to planet's radius)
G = gravitational constant (approximately 6.67430 × 10⁻¹¹ m³/kg/s²)
M = mass of the planet

To isolate the mass of the planet (M) in the equation, we can rearrange it as follows:

M = 4π²r³ / GT²

Plugging in the known values:

M = 4 * 3.14159² * (r³) / (6.67430 × 10⁻¹¹ * (240 * 60)²)

To find the radius of the planet (r), we can equate it to the maximum height reached by the rock since the cruise ship orbits at the same altitude.

Therefore, the mass of Planet Physics and the radius of Planet Physics can be calculated using the formulas provided.