A bald eagle flying horizontally at 48km/h drops it's prey from a height of 50m.
a)what is the prey's vertical velocity when it hits the ground?
b)when is the vertical speed greater than the horizontal speed?
a) v = sqrt(2 g h)
b) 48*10^3 m/3600 s = sqrt (2 g *distance fallen)
what is g and h supposed to be?
To find the answers to these questions, we'll need to use some basic physics principles. Let's break it down step by step:
a) To find the prey's vertical velocity when it hits the ground, we can use the equations of motion. We'll assume that there is no air resistance acting on the prey.
1. Determine the time it takes for the prey to reach the ground. We can use the equation for free fall: h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is time. Rearranging the equation, we get t = sqrt((2h)/g).
t = sqrt((2 * 50) / 9.8) ≈ 3.19 seconds
2. With the time (t) known, we can find the final vertical velocity (v) of the prey using the equation: v = gt, where g is the acceleration due to gravity.
v = 9.8 * 3.19 ≈ 31.26 m/s
Therefore, the prey's vertical velocity when it hits the ground is approximately 31.26 m/s.
b) To determine when the vertical speed is greater than the horizontal speed, we need to recognize that the horizontal speed remains constant throughout the motion.
Given that the eagle is flying horizontally at 48 km/h, we need to convert this velocity to m/s. 1 km/h is equal to 0.2778 m/s, so the horizontal speed is 48 * 0.2778 ≈ 13.333 m/s.
For the vertical speed to be greater than the horizontal speed, we need to determine the time it takes for the vertical velocity to surpass the horizontal velocity. As previously calculated, the prey takes about 3.19 seconds to hit the ground.
In this case, we observe that the vertical and horizontal speeds are not equal at any point during the prey's motion. Hence, the vertical speed never becomes greater than the horizontal speed.
Therefore, the vertical speed is not greater than the horizontal speed at any time during the motion of the prey.