Question

an astronaut on mars (mass 6.42×1023kg , radius 3.39×106m ) launches a probe straight upward from the surface at 3.00×103m/s . what is the maximum height above the surface that the probe reaches? neglect air resistance and the gravitational pull of the two small moons of mars.

Answer 1

The maximum height above the surface that the probe reaches on Mars is 1.17x10^6 meters.

Step-by-step explanation:

To find the maximum height above the surface that the probe reaches, we can use the concept of projectile motion. First, let's find the time it takes for the probe to reach its maximum height. We can use the equation:

tmax = V0y/g

where tmax is the time of flight, V0y is the initial vertical velocity, and g is the acceleration due to gravity. Since the probe is launched straight upward, the initial vertical velocity is the same as its launch velocity, which is 3.00x103 m/s. The acceleration due to gravity on Mars is 3.7 m/s2.

Plugging in the values, we have:

tmax = (3.00x103 m/s) / (3.7 m/s2)

Solving for tmax, we get:

tmax = 810.81 seconds

Now, let's find the maximum height by using the equation:

hmax = V0y x tmax - 0.5 x g x tmax2

Plugging in the values, we have:

hmax = (3.00x103 m/s) x (810.81 seconds) - 0.5 x (3.7 m/s2) x (810.81 seconds)2

Solving for hmax, we get:

hmax = 1.17x106 meters