Question

Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7m/s2.

a) 4.9 km/s
b) 5.7 km/s
c) 6.3 km/s
d) 7.1 km/s

Answer 1

To clear the Olympus Mons volcano on Mars, a projectile fired horizontally from a cannon would need an initial velocity greater than 4.3931 km/s. The correct answer is 4.9 km/s (option a).

Step-by-step explanation:

To determine the initial velocity required to clear the Olympus Mons volcano on Mars, we can use the projectile motion equations. Since the volcano is 25 km high and the cannonball will be fired horizontally, the time of flight can be calculated using the equation h = 0.5 * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time of flight. Solving for t, we get t = sqrt(2h/g). Substituting the given values, we have t = sqrt(2 * 25000 m / 3.7 m/s^2) = 70.94 s.

Now, we can determine the horizontal distance the cannonball will travel using the equation d = v * t, where d is the distance, v is the initial velocity, and t is the time of flight. We want the distance d to be greater than the radius of the volcano, which is 312 km. Therefore, we have d > 312000 m.

Substituting the values and solving for v, we get v > d / t = 312000 m / 70.94 s = 4393.1 m/s. Converting this to km/s, we get v > 4.3931 km/s.

Therefore, the correct answer is 4.9 km/s (option a).