When the Sun is directly overhead, a hawk dives toward the ground with a constant velocity of 4.80 m/s at 50.5° below the horizontal. Calculate the speed of her shadow on the level ground.
What i have done:
x= rcos(theta)
x=4.80m/s*cos(309.5)
x=3.05m
y=rsin(theta)
y=4.80m/s*sin(309.5)
y=-3.70m
i know to calculate speed the equation is v=d/t but there is no time stated in the problem... I came to the conclusion that the constant velocity is the speed, is that right?
Yes, when the problem states that the hawk is diving with a constant velocity of 4.80 m/s, it means that the magnitude of the velocity remains constant throughout the motion. In this case, the velocity is both the speed and magnitude of the hawk's motion.
To find the speed of the hawk's shadow on the level ground, you need to determine the horizontal component of the hawk's velocity (Vx) and the vertical component of the hawk's velocity (Vy).
From the given information, the hawk's velocity has an angle of 50.5° below the horizontal. To find the horizontal component (Vx), you can use the formula:
Vx = velocity * cos(angle)
Vx = 4.80 m/s * cos(50.5°)
Vx = 3.05 m/s
So, the horizontal component of the hawk's velocity is 3.05 m/s.
Next, to find the vertical component (Vy), you can use the formula:
Vy = velocity * sin(angle)
Vy = 4.80 m/s * sin(50.5°)
Vy = -3.70 m/s
Note that the negative sign indicates that the vertical component is directed downwards.
Now that you have the horizontal and vertical components of the velocities (Vx and Vy respectively), you can find the speed of the hawk's shadow on the level ground using the Pythagorean theorem:
Speed = sqrt(Vx^2 + Vy^2)
Speed = sqrt(3.05^2 + (-3.70)^2)
Speed = sqrt(9.3025 + 13.69)
Speed = sqrt(22.9925)
Speed ≈ 4.80 m/s
Therefore, the speed of the hawk's shadow on the level ground is approximately 4.80 m/s, which is equivalent to the magnitude of the hawk's constant velocity.