The mars rover opportunity approached Mars on January 24th, 2004 and was moving with a velocity of 5.4km/s when it hit the atmosphere on its way to the surface at Miridani Planum.
i)convert this speed to miles/hr.
ii) If it took the lander 6 minutes to hit the surface of Mars, what is the maximum height of the martian atmosphere?
iii)Why is this the maximum height and not the real height?
I got for i)1.9x 10^7m/hr
ii) 1.9 x 10^6m
1. Vi = 5.4km/s * 1mi/1.6km * 3600s/h = 12,150 mi/h.
2. h = Vi*t + 0.5g*t^2.
g = 3/8 * 9.8 = 3.675 m/s^2
t = 6min * 60s/min = 360 s.
h = 5400*360 + 0.5*3.675*360^2 = 2.18*10^6 m., max.
i) To convert the speed from kilometers per second (km/s) to miles per hour (mph), you can use the following conversions:
1 kilometer = 0.621371 miles
1 hour = 3600 seconds
So, the conversion can be done as follows:
5.4 km/s * (0.621371 miles/km) * (3600 s/hour) = 11,557.922 miles/hour
Therefore, the speed of the Mars Rover Opportunity is approximately 11,558 miles/hour.
ii) To find the maximum height of the Martian atmosphere, you can use the formula for free fall motion:
h = (1/2) * g * t^2
Where:
h = height
g = acceleration due to gravity
t = time taken
We know the time taken is 6 minutes, but it needs to be converted to seconds:
6 minutes * 60 seconds/minute = 360 seconds
Using the known value of acceleration due to gravity on Mars, which is approximately 3.71 m/s^2, we can now calculate the maximum height:
h = (1/2) * (3.71 m/s^2) * (360 s)^2
h ≈ 239,476.8 meters
Therefore, the maximum height of the Martian atmosphere is approximately 239,476.8 meters.
iii) The maximum height calculated above is actually the maximum height reached by the lander above the surface of Mars. However, it is not the true height of the Martian atmosphere. The atmosphere of Mars extends beyond this height, but the lander cannot travel any higher due to either atmospheric drag or its trajectory being too shallow to escape the gravitational pull of Mars. The true height of the Martian atmosphere extends much further, but it becomes increasingly thin and eventually merges with interplanetary space.