When the Sun is directly overhead, a hawk dives toward the ground with a constant velocity of 5.20 m/s at 51.5° below the horizontal. Calculate the speed of her shadow on the level ground.
5.20 m/s * cos(51.5º)
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To calculate the speed of the hawk's shadow on the level ground, we need to consider the motion of the hawk and the position of the sun. Here's how you can approach this problem:
1. Draw a diagram: Sketch a diagram to visualize the situation. Draw a horizontal line to represent the ground, a vertical line to represent the hawk (starting from the sun's position), and a diagonal line to represent the path of the hawk.
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------------------- <- Ground
2. Analyze the motion: The hawk is diving at a constant velocity of 5.20 m/s. The angle below the horizontal is given as 51.5°.
3. Break the velocity into components: Resolve the velocity of the hawk into horizontal and vertical components. The horizontal component is given by Vx = V * cos(theta), and the vertical component is given by Vy = V * sin(theta).
V = 5.20 m/s (velocity of the hawk)
theta = 51.5° (angle below the horizontal)
Vx = V * cos(theta) = 5.20 m/s * cos(51.5°)
Vy = V * sin(theta) = 5.20 m/s * sin(51.5°)
4. Calculate the time of flight: Since the hawk is diving directly downwards with constant velocity, the time of flight will be the same as the time it takes for the hawk to reach the ground. We can calculate this using the vertical component of velocity.
t = time of flight = - Vy / g
g = acceleration due to gravity = 9.8 m/s^2
5. Calculate the horizontal distance: The horizontal distance traveled by the hawk during the time of flight can be calculated using the horizontal component of velocity.
Dx = Vx * t
6. Calculate the speed of the shadow: The speed of the shadow is the horizontal distance traveled divided by the time of flight.
Speed of shadow = Dx / t
7. Substitute the values and calculate: Plug in the values for Vx, Vy, and t into the above equation and calculate the speed of the shadow.
Now you can go ahead and calculate the speed of the shadow by substituting the values from steps 3 and 4 into step 6.