Answer:
Mass of the planet = 1.48 × 10²⁵ Kg
Mass of the star = 5.09 × 10³⁰ kg
Explanation:
Given;
Diameter = 1.8 × 10⁷ m
Therefore,
Radius = 
= 
or
Radius of the planet = 0.9 × 10⁷ m
Rotation period = 22.3 hours
Radius of star = 2.2 × 10¹¹ m
Orbit period = 407 earth days = 407 × 24 × 60 × 60 seconds = 35164800 s
free-fall acceleration = 12.2 m/s²
Now,
we have the relation
g = 
g is the free fall acceleration
G is the gravitational force constant
M is the mass of the planet
on substituting the respective values, we get
12.2 = 
or
M = 1.48 × 10²⁵ Kg
From the Kepler's law we have
T² = 
on substituting the respective values, we get
35164800² = 
or
= 5.09 × 10³⁰ kg
The next step is to create research
Answer:
3.33 minutes (3 minutes and 20 seconds)
Explanation:
Speed of the runner = s = 5 m/s
We need to calculate how will it take for runner to complete 1 km. We have the speed, the distance and we need to find the time. Before performing any calculations, we must convert the values to same units.
Speed is in m/s and distance is in kilometers. So we have to either convert speed to km/s or distance into meters. In this case, converting distance into meters would be a convenient option.
1 kilo meters = 1000 meters
The distance, speed and time are related by the equation:
Distance = Speed x Time
So,
Time = Distance/Speed
Using the values, we get:
t = 1000/5
t = 200 seconds
This means, the runner can complete 1 kilometers in 200 seconds. Since, there are 60 seconds in a minute, we can convert this time to minutes, by dividing it by 60. i.e.
Thus, it will take the runner 3.33 minutes (3 minutes and 20 seconds) to travel 1 km.
Explanation:
It is given that, a batter hits a pop-up to a fielder 93 m away, range of the projectile, R = 93 m
The ball remains in the air for 5.4 s, the time of flight is 5.4 s
Time of flight : 
Maximum height of the projectile : 
We need to find H.
So,
So, it will rise to a height of 35.72 m.
