Chameleons catch insects with their tongues, which they can extend to great lengths at great speeds. A chameleon is aiming for an insect at a distance of 22 cm. The insect will sense the attack and move away 60 ms after it begins. In the first 60 ms, the chameleon’s tongue accelerates at 250 m/s2 for 20 ms, then travels at constant speed for the remaining 40 ms. Does its tongue reach the 22 cm extension needed to catch the insect during this time?

Question

Chameleons catch insects with their tongues, which they can extend to great lengths at great speeds. A chameleon is aiming for an insect at a distance of 22 cm. The insect will sense the attack and move away 60 ms after it begins. In the first 60 ms, the chameleon’s tongue accelerates at 250 m/s2 for 20 ms, then travels at constant speed for the remaining 40 ms. Does its tongue reach the 22 cm extension needed to catch the insect during this time?

Answer 1

the average velocity during the acceleration is 125m/s

distance=125*.02cm+250*.04=
= 5cm+10cm
check that, I was guessing he caught it.

Answer 2

To determine whether the chameleon's tongue reaches the 22 cm extension needed to catch the insect, we need to calculate the distance traveled by the tongue during the given time period.

Let's break down the information given:

Distance to be covered = 22 cm
Time for the insect to sense and move away = 60 ms
Acceleration of the tongue = 250 m/s²
Time for the tongue to accelerate = 20 ms
Remaining time for the tongue to travel at a constant speed = 40 ms

First, let's calculate the distance covered during the acceleration phase:

To calculate distance covered during constant acceleration, we use the formula:

d = (1/2) * a * t²

where d is the distance, a is the acceleration, and t is the time.

Using the values given:

d = (1/2) * 250 m/s² * (20 ms / 1000)²
d = (1/2) * 250 m/s² * 0.02²
d = (1/2) * 250 m/s² * 0.0004
d = 0.5 * 0.1
d = 0.05 meters or 5 centimeters

During the acceleration phase, the tongue covers a distance of 5 centimeters.

Next, we need to calculate the distance traveled during the constant speed phase. Since the tongue is traveling at a constant speed, we can use the formula:

d = v * t

where d is the distance, v is the velocity, and t is the time.

The velocity is constant, so we need to calculate it:

With an acceleration of 250 m/s² and a time of 20 ms:

v = a * t
v = 250 m/s² * (20 ms / 1000)
v = 250 m/s² * 0.02
v = 5 m/s

Now we can calculate the distance traveled during the constant speed phase:

d = 5 m/s * (40 ms / 1000)
d = 5 m/s * 0.04
d = 0.2 meters or 20 centimeters

During the constant speed phase, the tongue covers a distance of 20 centimeters.

Adding up the distances covered during the acceleration phase and the constant speed phase:

Total distance = 5 cm + 20 cm
Total distance = 25 centimeters

Therefore, the tongue reaches a total extension of 25 centimeters, which is more than the 22 centimeters needed to catch the insect. So, yes, the chameleon's tongue does reach the required extension during this time.