Question

question 10
a satellite is placed in a circular orbit to observe the surface of mars from an altitude of 144 km (kilometer). the equatorial radius of mars is 3397 km. if the speed of the satellite is 3480 m/s, what is the magnitude of the centripetal acceleration of the satellite? hint: the total radius (r) is the radius of mars + altitude above the surface; 1 km = 1,000 m.

2.60 m/s²
2.99 m/s²
2.17 m/s²
4.05 m/s²
3.42 m/s²

Explanation:

Step1: Calculate total radius

First, convert km to m. Mars radius $3397$ km = $3397\times1000 = 3397000$ m, altitude $144$ km=$144\times1000 = 144000$ m. Total radius $r=3397000 + 144000=3541000$ m.

Step2: Use centripetal - acceleration formula

The formula for centripetal acceleration is $a_c=\frac{v^{2}}{r}$, where $v = 3480$ m/s and $r = 3541000$ m. So $a_c=\frac{3480^{2}}{3541000}=\frac{12110400}{3541000}\approx3.42$ m/s².

Answer:

$3.42$ m/s² (the option corresponding to $3.42$ m/s² in the multiple - choice list)