Could you please check my work and help me with two of the problems.
An airplane that flies at 100 km/h with a 10 km/h tailwind travels at 110 km/h relative to the ground. If it instead flies into a 10 km/h headwind, its groundspeed is
100km/h-10km/h = 90 km/h
The average speed of a horse that gallops a distance of 10 kilometers in a time of 30 minutes is? (This one I don't understand, I know the formula to find average speed is is average speed= distance traveled/time of travel)
What is the acceleration of a car that maintains a constant velocity of 100 km/hr for 10 seconds? (For this one don't I have to get the same units, this is how I started, but not too sure where to go afterward: (100 km/hr)(1000 km/hr)(1/3600 s)= 27.8 m/s)
The airplane problem is correct.The horse speed is 10 km/30 min which would make it 20 km/hr. That is solved as 10km/0.5hr = 20 km/hr. The problem doesn't ask for a particular unit.
The third problem I will leave for others.
For the second problem, to find the average speed, you need to convert the time to the same units as the distance. In this case, the distance is in kilometers and the time is in minutes. So, you need to convert the time to hours (since speed is typically measured in km/h).
We know that there are 60 minutes in an hour, so to convert 30 minutes to hours, you divide it by 60:
30 minutes ÷ 60 = 0.5 hours
Now that we have the time in hours, we can use the formula for average speed:
average speed = distance traveled ÷ time of travel
Plugging in the values, we have:
average speed = 10 km ÷ 0.5 h = 20 km/h
Therefore, the average speed of the horse that gallops a distance of 10 kilometers in a time of 30 minutes is 20 km/h.
For the third problem, you are correct in wanting to convert the velocity from km/hr to m/s to ensure that the units are consistent for acceleration.
First, you need to convert km/hr to m/s. There are 1000 meters in a kilometer and 3600 seconds in an hour. So, you can convert as follows:
(100 km/hr) x (1000 m/km) ÷ (3600 s/hr) = 27.8 m/s
Now that you have converted the velocity, you can use the formula for acceleration:
acceleration = change in velocity ÷ time
In this case, the car maintains a constant velocity of 100 km/hr for 10 seconds, so the change in velocity is 0 (since it doesn't change).
Plugging in the values, we have:
acceleration = 0 m/s ÷ 10 s = 0 m/s^2
Therefore, the acceleration of the car is 0 m/s^2 since it maintains a constant velocity.