Question

A biologist who has been studying herd movements in elephants just finished spending several hours with the herd. The elephants are now moving due east at 3 kilometers per hour. The biologist, meanwhile, is driving due west to base camp at a rate of at 49 kilometers per hour. In how long will the biologist be 3 kilometers from the herd?

Answer 1

The biologist will take approximately 0.234 seconds to be 3 kilometers from the herd.

Step-by-step explanation:

To find out how long it will take for the biologist to be 3 kilometers from the herd, we need to determine the relative velocity between the biologist and the herd. Since the biologist is driving west and the herd is moving east, their velocities are in opposite directions. We can subtract the velocity of the herd from the velocity of the biologist to find the relative velocity: 49 km/h - 3 km/h = 46 km/h.

Now, we can use the formula for time: time = distance / velocity. In this case, the distance is 3 kilometers and the velocity is 46 km/h. Plugging these values into the formula, we get: time = 3 km / 46 km/h. Converting the units to be consistent, we have: time = 3 km / (46,000 m / 3600 s). Simplifying the expression gives us: time = 3 km / (46,000 / 3600) s = 3 km / 12.778 s = 0.234 seconds.

Therefore, it will take the biologist approximately 0.234 seconds to be 3 kilometers from the herd.