question #1:
Margret has just enough gas in her speedboat to get to the marina,an upstream journey that takes 4.0 hours. finding it closed for the season, she spends the next 8.0 hours floating back downstream to her shack. the entire trip took 12.0 hours; how long would it have taken if she had bought gas at the marina?
Question #2:
a BMW M3 sports car can accelerate in third gear from 48.3 km/h to 80.5 km/h in 3.7 s. (a) what is the average acceleration of this car in m/s(squared...dont know how to type that )? (b) if the car continued at this acceleration for another second, how fast would it be moving?
Can someone help explain how to get the answer to this problem instead of just giving me the answer. can you tell me what equations you used as well.thanks
Margret has just enough gas in her speedboat to get to the marina,an upstream journey that takes 4.0 hours. finding it closed for the season, she spends the next 8.0 hours floating back downstream to her shack. the entire trip took 12.0 hours; how long would it have taken if she had bought gas at the marina?
Question #2:
a BMW M3 sports car can accelerate in third gear from 48.3 km/h to 80.5 km/h in 3.7 s. (a) what is the average acceleration of this car in m/s(squared...dont know how to type that )? (b) if the car continued at this acceleration for another second, how fast would it be moving?
Can someone help explain how to get the answer to this problem instead of just giving me the answer. can you tell me what equations you used as well.thanks
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1) Assuming a constant speed for both current and boat.
A 'trip' is defined as a single length over the distance from shack to marina.
Current speed is Distance / Time or 1 trip / 8 hours.
During the upstream trip the current carries the boat downstream at the same time it's going upstream. So "shore speed" is slower than "water speed". Same concept as a headwind.
Boat upstream distance is trip distance + (current * boat time)
So current distance during upstream trip is 1/2 trip. So total distance covered is 3/2 trips.
Boat speed is total distance / time.
or 3 trips / 8 hours
When running the boat makes 3x the speed of the current. This is demonstrated in that it not only overcomes the current's speed, but makes the same journey in half the time.
Now if she had had gas, the current's speed would have been added to the boat's instead of subtracted.
So downstream speed would have been 4 trips in 8 hours. Or one trip in two hours.
So it would only have taken 2 hours to get back if she had managed to buy gas.
2) Avg accel
The car accelerates 32.2 km/h (velocity change) over 3.7 seconds (time). Find meters per second velocity change.
32.2 km/hr * 1/3600 hr/sec * 1000 m/km
8.94444 m/sec. over 3.7 seconds
8.9444/3.7 = 2.4174 m/sec^2 avg accel
Velocity is accel * time. 2.4174 * 1 = 2.4174 m/sec.
Find km/hr.
2.4174 * 3600 / 1000 = ~ 8.7 km an hour additional.
So 80.5+8.7 = 89.2 km/hr.
A 'trip' is defined as a single length over the distance from shack to marina.
Current speed is Distance / Time or 1 trip / 8 hours.
During the upstream trip the current carries the boat downstream at the same time it's going upstream. So "shore speed" is slower than "water speed". Same concept as a headwind.
Boat upstream distance is trip distance + (current * boat time)
So current distance during upstream trip is 1/2 trip. So total distance covered is 3/2 trips.
Boat speed is total distance / time.
or 3 trips / 8 hours
When running the boat makes 3x the speed of the current. This is demonstrated in that it not only overcomes the current's speed, but makes the same journey in half the time.
Now if she had had gas, the current's speed would have been added to the boat's instead of subtracted.
So downstream speed would have been 4 trips in 8 hours. Or one trip in two hours.
So it would only have taken 2 hours to get back if she had managed to buy gas.
2) Avg accel
The car accelerates 32.2 km/h (velocity change) over 3.7 seconds (time). Find meters per second velocity change.
32.2 km/hr * 1/3600 hr/sec * 1000 m/km
8.94444 m/sec. over 3.7 seconds
8.9444/3.7 = 2.4174 m/sec^2 avg accel
Velocity is accel * time. 2.4174 * 1 = 2.4174 m/sec.
Find km/hr.
2.4174 * 3600 / 1000 = ~ 8.7 km an hour additional.
So 80.5+8.7 = 89.2 km/hr.