1. An eagle flying at 15 m/s at an altitude of 180 m drops its prey. The trajectory of the falling prey is parabolic and can be represented by the equation until it hits the ground, where y is the height above the ground and x is the horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.

The distance traveled by the prey from the time it is dropped until the time it hits the ground is 64.2m

Explanation:

Since the trajectory of the falling prey is parabolic, the motion of the prey in air is a projectile motion.

In projectile, the distance covered by the prey in the horizontal direction is the RANGE.

Range is expressed mathematically as U²Sin2theta/2g OR U√2H/g

Since we are given the altitude and the velocity of the eagle, we will apply:

Range = U√2H/g where:

U is the velocity

H is the maximum height (altitude)

g is the acceleration due to gravity

Given U =15m/s

H = 180m

g = 9.81m/s²

Range = 15× √180/9.81

Range = 15 × √18.35

Range = 15 × 4.28

Range = 64.2m