A zebra sees a lion 300 m to his right. The zebra starts running at 25 KpH straight ahead to get away. At this point the lion launches himself on an intercept course at the zebra at a speed of 31 KpH.
a. At what angle does the lion launch himself?
b. If both animals continue to travel straight, how long does it take the lion to catch the zebra?
To find the angle at which the lion launches himself, we can use trigonometry. Let's consider the scenario when the zebra starts running. At this point, the initial distance between the lion and the zebra forms a right triangle. The lion's position is the hypotenuse, the distance between the lion and the zebra is the adjacent side, and the distance the zebra runs is the opposite side.
a. To find the angle, we can use the tangent function, which is equal to the opposite side divided by the adjacent side:
tangent(angle) = opposite / adjacent
tangent(angle) = 300 / 25
tangent(angle) = 12
Using the inverse tangent function (tan^(-1)), we can find the angle:
angle = tan^(-1)(12)
angle ≈ 86.41 degrees
Therefore, the lion launches himself at an angle of approximately 86.41 degrees.
b. To find the time it takes for the lion to catch the zebra, we need to determine the time it takes for each animal to run the same distance. Since both animals travel in a straight line, we can use the formula: time = distance / speed.
The zebra's distance traveled is the same as the distance between the lion and the zebra, which is 300 meters. The zebra's speed is given as 25 km/h, or 25000 meters per hour. Thus,
time taken by zebra to cover 300 m = 300 m / 25000 m/h
time taken = 0.012 hours
The lion's speed is given as 31 km/h, or 31000 meters per hour. Therefore,
time taken by lion to cover 300 m = 300 m / 31000 m/h
time taken = 0.00967 hours
As the lion's time is smaller, it will catch the zebra before the zebra completes its 300-meter run.