Question

In the savannah of Africa a gazelle is running in a straight line with constant velocity of 16m/s. A Cheetah is startled by the gazelle when she runs past. At the instant the Cheetah and gazelle are side by side. The cheetah accelerates after the gazelle from rest at 12m/s². So how much does it take for cheetah to catch-up the gazelle?

Answer 1

To calculate how long it will take the cheetah to catch up to the gazelle, we can use the equation of motion for the cheetah. The cheetah starts from rest and accelerates at a rate of 12 m/s². The gazelle is running with a constant velocity of 16 m/s. It will take the cheetah approximately 0.67 seconds to catch up to the gazelle.

Step-by-step explanation:

To calculate how long it will take the cheetah to catch up to the gazelle, we can use the equation of motion for the cheetah. The cheetah starts from rest and accelerates at a rate of 12 m/s². The gazelle is running with a constant velocity of 16 m/s. Let's denote the time it takes for the cheetah to catch up to the gazelle as t.

Using the equation of motion for the cheetah, we have:

s = ut + \frac{1}{2}at^2

where s is the displacement of the cheetah, u is its initial velocity (0 m/s), a is the acceleration (12 m/s²), and t is the time.

Since the cheetah starts from rest, its initial velocity u is 0. Therefore, the equation simplifies to:

s = \frac{1}{2}at^2

We can also use the equation of motion for the gazelle:

s = vt

where v is the velocity of the gazelle (16 m/s).

Since the gazelle is running at a constant velocity, its displacement s is also equal to vt. Therefore, we can equate the two equations:

\frac{1}{2}at^2 = vt

Simplifying the equation:

\frac{1}{2} \times 12 \times t^2 = 16 \times t

Dividing both sides by t and multiplying by 2:

24t = 16

Now we can solve for t:

t = \frac{16}{24} = \frac{2}{3}

Therefore, it takes the cheetah approximately 0.67 seconds to catch up to the gazelle.