When the Sun is directly overhead, a hawk
dives toward the ground at a speed of
3.07 m/s.
If the direction of his motion is at an angle
of 57.2
◦
below the horizontal, calculate the
speed of his shadow along the ground.
Answer in units of m/s
To calculate the speed of the hawk's shadow along the ground, we can use basic trigonometry.
Let's break down the given information:
- The hawk's speed is given as 3.07 m/s.
- The direction of the hawk's motion is at an angle of 57.2° below the horizontal.
To find the speed of the hawk's shadow, we need to consider the vertical and horizontal components of the hawk's motion.
The vertical component represents the change in height, which is perpendicular to the ground. The horizontal component represents the change in distance along the ground.
Since the hawk is diving downward, the vertical component of its motion is given by:
Vertical component = hawk's speed * sine(angle)
Using the given values, we can calculate the vertical component:
Vertical component = 3.07 m/s * sin(57.2°)
Next, we need to find the horizontal component of the hawk's motion. This will give us the speed of the shadow along the ground. The horizontal component is given by:
Horizontal component = hawk's speed * cosine(angle)
Using the given values, we can calculate the horizontal component:
Horizontal component = 3.07 m/s * cos(57.2°)
Finally, the speed of the shadow along the ground is equal to the magnitude of the horizontal component:
Speed of shadow along the ground = absolute value of the horizontal component
Calculating the numerical solution:
Vertical component = 3.07 m/s * sin(57.2°) = 2.607 m/s (rounded to three decimal places)
Horizontal component = 3.07 m/s * cos(57.2°) = 1.582 m/s (rounded to three decimal places)
Speed of shadow along the ground = absolute value of the horizontal component = |1.582 m/s| = 1.582 m/s
Therefore, the speed of the hawk's shadow along the ground is approximately 1.582 m/s.