When the Sun is directly overhead, a hawk
dives toward the ground at a speed of
6.97 m/s.
If the direction of his motion is at an angle
of 34.1 below the horizontal, calculate the
speed of his shadow along the ground.
Answer in units of m/s
let x be the distance along the ground.
then cosine 34.1= vx/6.97 solve for vx.
It is more fun and challenging if the sun were at some angle.
thanks
5.77
To calculate the speed of the hawk's shadow along the ground, we need to use the concept of trigonometry. Here's how you can approach this problem:
1. Firstly, we need to determine the horizontal component of the hawk's velocity. We can find this by multiplying the hawk's diving speed (6.97 m/s) by the cosine of the angle between its motion and the horizontal direction. Since the angle is given as 34.1 degrees below the horizontal, we can determine the horizontal component of velocity (Vx) as follows:
Vx = 6.97 m/s * cos(34.1°)
2. Next, we need to determine the vertical component of the hawk's velocity. This component will affect the shadow's speed along the ground. To find the vertical component of velocity (Vy), we can multiply the hawk's diving speed (6.97 m/s) by the sine of the angle between its motion and the horizontal direction:
Vy = 6.97 m/s * sin(34.1°)
3. Now that we have both components of the hawk's velocity, we can use them to calculate the speed of the shadow along the ground. The speed of the shadow is equal to the horizontal component of the hawk's velocity (Vx) because the shadow moves only along the ground. Therefore, the speed of the shadow along the ground would be:
Speed of shadow along the ground = Vx
Simply substitute the value of Vx from step 1 to get the final answer.
Calculating the values using a calculator, we have:
Vx ≈ 6.97 m/s * cos(34.1°) ≈ 5.79 m/s
Therefore, the speed of the hawk's shadow along the ground is approximately 5.79 m/s.