When the Sun is directly overhead, a hawk dives toward the ground with a constant velocity of 4.45 m/s at 61.5° below the horizontal. Calculate the speed of her shadow on the level ground.
To calculate the speed of the hawk's shadow on the level ground, we can use trigonometry.
First, let's break down the motion of the hawk into horizontal and vertical components. The constant velocity of the hawk is given as 4.45 m/s at an angle of 61.5° below the horizontal.
The vertical component of velocity can be calculated as follows:
Vertical velocity = 4.45 m/s * sin(61.5°)
Next, let's consider the shadow. When the Sun is directly overhead, the rays of sunlight are perpendicular to the ground. Therefore, the shadow's movement will be purely horizontal.
The horizontal component of velocity will be equal to the hawk's horizontal velocity:
Horizontal velocity = 4.45 m/s * cos(61.5°)
Now, the speed of the shadow can be determined by using the Pythagorean theorem:
Speed of shadow = √(Vertical velocity^2 + Horizontal velocity^2)
Let's calculate:
Vertical velocity = 4.45 m/s * sin(61.5°) ≈ 3.89 m/s
Horizontal velocity = 4.45 m/s * cos(61.5°) ≈ 2.03 m/s
Speed of shadow = √(3.89 m/s^2 + 2.03 m/s^2) ≈ √15.13 m^2/s^2 ≈ 3.88 m/s
Therefore, the speed of the hawk's shadow on the level ground is approximately 3.88 m/s.