A cheetah can maintain its maximum speed of 120 km/hr for 38 seconds. What minimum distance must a gazelle running 74 km/hr be ahead of the cheetah to escape?
A) 417.2 m
B) 3778 m
C) 624.3 m
D) 485.6 m
E) 1748 m
Dc = 120,000m/h * (38/3600)h = 1266.7 m. = Distance covered by cheetah.
Dg + 74,000m/h*(38/3600))h = 1266.7.
Dg = 485.6 m.
at t=38, one wants the separation be 1 meter.
distance(38)=speedgazelle*38-speedcheeta(38)+intialseparation
change the speeds to m/s, then
1=xxx*38-YYY*38+initialseparation
solve for separation
To solve this problem, we need to calculate the distance the cheetah can cover in 38 seconds at its maximum speed of 120 km/hr. Then we can find how much distance the gazelle should be ahead of the cheetah to escape.
First, let's calculate the distance covered by the cheetah in 38 seconds. We can use the formula:
Distance = Speed × Time
Since the cheetah's speed is given in km/hr, we need to convert it to meters per second (m/s) to match the time in seconds. We know that 1 km = 1000 m and 1 hr = 3600 s.
Cheetah's speed in m/s = (120 km/hr) × (1000 m/km) / (3600 s/hr)
= (120 × 1000) / 3600
= 33.33 m/s (rounded to two decimal places)
Now, let's calculate the distance covered by the cheetah in 38 seconds:
Distance = (Cheetah's speed) × (Time)
= 33.33 m/s × 38 s
= 1266.54 m (rounded to two decimal places)
Therefore, the cheetah can cover a distance of approximately 1266.54 meters in 38 seconds.
Next, we need to find out the minimum distance the gazelle should be ahead of the cheetah to escape. To determine this, we subtract the distance covered by the cheetah from the distance covered by the gazelle in the same time.
The gazelle's speed is given as 74 km/hr, so let's convert it to m/s:
Gazelle's speed in m/s = (74 km/hr) × (1000 m/km) / (3600 s/hr)
= (74 × 1000) / 3600
= 20.56 m/s (rounded to two decimal places)
Now, let's calculate the distance covered by the gazelle in 38 seconds:
Distance = (Gazelle's speed) × (Time)
= 20.56 m/s × 38 s
= 780.08 m (rounded to two decimal places)
Finally, to find the minimum distance the gazelle should be ahead of the cheetah, we subtract the distance covered by the cheetah from the distance covered by the gazelle:
Minimum distance = (Distance covered by gazelle) - (Distance covered by cheetah)
= 780.08 m - 1266.54 m
= -486.46 m (negative value indicates that the gazelle was caught)
From the calculation, we can see that the gazelle was caught by the cheetah. Therefore, it is not possible for the gazelle to escape from the cheetah in this situation.
Hence, the correct answer would be None of the above.
so, with that i got 484.26.
they obviously solved for separation to be 0 at 38s, which doesn't make sense because the gazelle would die.. but do you think d then is the right answer?