An interplanetary spaceship lands on a planet with negligible atmosphere and fires three projectiles at the same angle carrying exploratory bots, but at different initial velocities. After the bots land on the surface their distances are measured and the data recorded as follows:
Velocity in m/s |
Distance in m |
400 |
38 098 |
600 |
85 692 |
800 |
152 220 |
? |
300 000 |
At what speed should the projectile carrying the 4th bot be fired in order for it to land 300 km from the spacecraft?
Analysis:
For this problem we need to understand the trajectory of the projectile. Since the atmosphere on the explored planet is weak, the trajectory is almost equivalent to the ballistic curve without the air drag. The distance d traveled by an object fired from a point on the ground is approximately (neglecting the curving of...