Fox sees a piece of carrion being thrown from nest and rushes to it. Nest is 14.0 m high and carrion is thrown with a horizontal velocity of 1.5m/s. Fox is 7.0 m from the base of tree. What is magnitude of fox's average velocity if it grabs carrion in its mouth just as it touches ground?
Dr Bob said I should find time it takes something to fall 14 meters
During that time, how far horizontally does it goes, given horizontal velocity. Then deal with fox-how fast doe he have to go to cover 7 m in the falling time
answers were:
1.7 m/s
3.5 m/s
4.2 m/s
2.6 m/s
I think the answer is 2.6 m/s
Is that correct -if not please help
I have spent the greater part of the day trying to do this
Let me see your work.
To find the magnitude of the fox's average velocity, we need to calculate the time it takes for the carrion to fall to the ground.
First, let's find the time it takes for the carrion to fall 14.0 meters. We can use the equation of motion for vertical motion, which is:
y = v₀t + (1/2)at²
In this case, the initial vertical velocity (v₀) is 0 m/s because the carrion is dropped vertically. The acceleration (a) due to gravity is approximately 9.8 m/s². The final vertical position (y) is -14.0 m (negative because it's downward).
Plugging in the values into the equation, we can solve for time (t):
-14.0 = 0 + (1/2)(9.8)t²
Simplifying the equation:
-14.0 = 4.9t²
Dividing both sides by 4.9:
-2.857 = t²
Finding the square root of both sides:
t ≈ -1.69
Since time cannot be negative in this context, we discard the negative solution. Therefore, the time it takes for the carrion to fall 14.0 meters is approximately 1.69 seconds.
Next, let's calculate the horizontal distance the carrion travels given its horizontal velocity of 1.5 m/s. We can use the equation:
d = vt
Where d is the distance and v is the horizontal velocity. Plugging in the values:
d = (1.5)(1.69)
Simplifying the equation:
d ≈ 2.54
Therefore, the carrion travels approximately 2.54 meters horizontally during the falling time.
Finally, we need to determine how fast the fox has to go to cover 7.0 meters in the falling time of 1.69 seconds. We can use the equation:
v = d/t
Where v is the velocity, d is the distance, and t is the time. Plugging in the values:
v = 7.0/1.69
Simplifying the equation:
v ≈ 4.14
Therefore, the magnitude of the fox's average velocity to cover 7.0 meters in the falling time is approximately 4.14 m/s.
None of the answer choices provided match with our calculation. The correct answer seems to be missing. However, based on the calculations, the magnitude of the fox's average velocity should be around 4.14 m/s, not 2.6 m/s.
To solve this problem, you need to break it down into several steps. Let's go through the process step-by-step.
Step 1: Find the time it takes for the carrion to fall 14 meters.
We can use the equation for vertical motion, using the formula 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 the time.
Given that the height is 14.0 meters, we can rearrange the formula to solve for t:
14 = (1/2)(9.8)t^2
t^2 = 14 / (0.5 * 9.8)
t^2 = 2.857
t ≈ √2.857
t ≈ 1.69 seconds
Therefore, it takes approximately 1.69 seconds for the carrion to fall 14 meters.
Step 2: Calculate the horizontal distance traveled by the carrion.
The horizontal distance traveled by the carrion can be found using the formula d = vt, where d is the distance, v is the horizontal velocity, and t is the time.
Given that the horizontal velocity is 1.5 m/s and the time is 1.69 seconds, we can calculate the distance:
d = 1.5 m/s * 1.69 s
d = 2.535 meters
Therefore, the carrion travels approximately 2.535 meters horizontally.
Step 3: Determine the fox's average velocity.
The fox needs to cover a horizontal distance of 7.0 meters in the same time period as the carrion falls. To calculate the fox's average velocity, divide the horizontal distance by the time.
Average velocity = 7.0 m / 1.69 s
Average velocity ≈ 4.14 m/s
Therefore, the magnitude of the fox's average velocity, if it grabs the carrion just as it touches the ground, is approximately 4.14 m/s.
So, the correct answer is not 2.6 m/s, but rather 4.14 m/s.