When the Sun is directly overhead, a hawk dives towards the ground with a constant velocity of 5.1 m/s at 45° below the horizontal. Calculate the speed of its shadow on the level ground.
m/s
The sun is far enough away that you can assume it remains directly overhead. Luckily also a flat rather than curved earth is assumed. Therefore the shadow (which remains directly under the bird) moves at the horizontal component of the velocity of the bird. 5.1 cos 45 = 5.1* (1/2) sqrt 2
To calculate the speed of the hawk's shadow on the level ground, we can break down the velocity of the hawk into horizontal and vertical components.
Given:
- Velocity of the hawk = 5.1 m/s
- Angle below the horizontal = 45°
First, let's find the horizontal and vertical components of the velocity:
Horizontal component:
The horizontal component of the hawk's velocity is given by the formula: Vx = V × cosθ
where Vx is the horizontal component of the velocity, V is the magnitude of the velocity, and θ is the angle below the horizontal.
Vx = 5.1 m/s × cos(45°) = 5.1 m/s × (√2/2) = 5.1 m/s × 0.707 = 3.61 m/s
Vertical component:
The vertical component of the hawk's velocity is given by the formula: Vy = V × sinθ
where Vy is the vertical component of the velocity, V is the magnitude of the velocity, and θ is the angle below the horizontal.
Vy = 5.1 m/s × sin(45°) = 5.1 m/s × (√2/2) = 5.1 m/s × 0.707 = 3.61 m/s
Since the Sun is directly overhead, the horizontal component of the hawk's velocity will determine the speed of its shadow on the level ground. Therefore, the speed of the shadow on the level ground is:
3.61 m/s.