A cheetah running at 30 m/s is pursuing a zebra going in a straight line at 14 m/s. If the zebra has a 35 m head start, how much time does it take for the zebra to catch up?
(Please show all work. I know the answer, but I need the step by step instruction to understand.)
Xc = cheetah distance traveled = 30 t
Xz = zebra location = 35 + 14 t
Set Xc = Xz and solve for t
30t = 35 + 14t when they meet
16t = 35
t = 2.1875 s
Well, let's calculate the relative speed of the cheetah with respect to the zebra first. The cheetah is running at 30 m/s, while the zebra is moving at 14 m/s. To find the relative speed, we just subtract the speeds:
Relative speed = Cheetah's speed - Zebra's speed = 30 m/s - 14 m/s = 16 m/s.
Now, we need to consider the distance the zebra needs to cover to catch up to the cheetah. Since the zebra has a 35 m head start, it means the distance between them is 35 m initially.
Now, let's figure out how much time it takes for the zebra to cover that distance at a relative speed of 16 m/s:
Time = Distance / Speed = 35 m / 16 m/s = 2.1875 seconds.
So it takes approximately 2.1875 seconds for the zebra to catch up to the cheetah.
Now, that's pretty impressive for a zebra! Maybe they should consider a career in sprinting!
To find out how much time it takes for the cheetah to catch up to the zebra, we need to determine when they will be at the same position.
Let's assume that the time it takes for them to meet is t seconds.
During this time, the cheetah will have traveled a distance of 30t meters and the zebra will have traveled a distance of 14t + 35 meters (taking into account the 35 m head start).
Since they will be at the same position when they meet, we can set up the following equation:
30t = 14t + 35
We can now solve this equation step by step:
1. Subtract 14t from both sides to isolate the variables:
30t - 14t = 35
2. Simplify the equation:
16t = 35
3. Divide both sides by 16 to solve for t:
t = 35 / 16
Now we can calculate the value of t to find the time it takes for the zebra to be caught by the cheetah.
Using a calculator or long division, we can find that t ≈ 2.1875 seconds.
So, it takes approximately 2.1875 seconds for the zebra to be caught by the cheetah.
To find out how much time it takes for the cheetah to catch up to the zebra, we can start by determining the distance between them. Since the zebra has a 35 m head start, the distance the cheetah needs to cover is 35 m less than the distance the zebra has to cover to maintain the same distance between them.
Let's call the time it takes for the cheetah to catch up to the zebra as "t" seconds. During this time, the cheetah will cover a distance equal to 30 m/s multiplied by "t" seconds (30t), while the zebra will cover a distance equal to 14 m/s multiplied by "t" seconds (14t).
Since the distance the cheetah needs to cover is 35 m less than the distance the zebra has to cover, we can set up the following equation:
30t = 14t + 35
Now, let's solve this equation step by step:
1. Start by subtracting 14t from both sides of the equation:
30t - 14t = 14t + 35 - 14t
16t = 35
2. Divide both sides of the equation by 16 to isolate the "t" term:
(16t)/16 = 35/16
t = 35/16
3. Simplify the right side of the equation:
t ≈ 2.1875
Therefore, it takes approximately 2.1875 seconds for the zebra to be caught by the cheetah.