A cheetah can run approximately 100 km/hr and a gazelle at 80.0 km/hr. If both animals are running at full speed, with the gazelle 70.0 m ahead, how long before the cheetah catches its prey?
time = t
distance in meters = 1,000*distance in km
distance covered by cheetah = d
distance covered by gazelle = d-70
d = 100,000 t
d-70 = 80,000 t
so
70 + 80,000 t = 100,000 t
20,000 t = 70
t = 7/2000 hours
in seconds (3600 s/h)
t in seconds = 7*3600/2000 = 12.6 seconds
thank you so much.
Well, let's do the math. The cheetah is running 20 km/hr faster than the gazelle, which means it gains 20 km/hr on the gazelle. Now we need to convert that to meters per second, because, you know, metric is the way to go. So, 20 km/hr is approximately 5.6 m/s faster.
Now, to catch up to the gazelle, the cheetah needs to cover that 70.0 meters of distance between them. We can divide that distance by the speed difference of 5.6 m/s (that's 70.0m / 5.6m/s) and we get approximately 12.5 seconds.
So, the cheetah will catch up to its prey in approximately 12.5 seconds. But hey, don't worry, it's just a game of cat and mouse... or should I say, cat and gazelle!
To find out how long it takes for the cheetah to catch the gazelle, we need to calculate the time it takes for the cheetah to cover the 70.0 m distance between them.
First, let's convert the speeds to meters per second for consistency. Since 1 km is equal to 1000 m and 1 hour is equal to 3600 seconds, we can convert the speeds as follows:
Cheetah speed = 100 km/hr = (100 * 1000 m) / (3600 s) = 27.8 m/s
Gazelle speed = 80.0 km/hr = (80.0 * 1000 m) / (3600 s) = 22.2 m/s
Now, we can use the equation: distance = speed * time to get the time it takes for the cheetah to cover the 70.0 m distance.
70.0 m = (27.8 m/s - 22.2 m/s) * time
Subtracting the gazelle's speed from the cheetah's speed gives the effective relative speed between them.
70.0 m = 5.6 m/s * time
To find the time, we divide both sides of the equation by 5.6 m/s:
time = 70.0 m / 5.6 m/s = 12.50 s
Therefore, it takes approximately 12.50 seconds for the cheetah to catch the gazelle.