Let's give it a whirl .....
At A, coaster is only associated with potential energy.
At B, coaster is associated with kinetic as well as potential energy.
Since the track is frictionless, no energy will be lost when coaster reaches from point A to point B. Therefore, according to conservation of energy, total energy at A should be equal to total energy at B.
Total energy at A = mgh = mg(12)
Total energy at B = mgh+ mv²/2 = mg(2) + mv²/2
∴12mg = 2mg + mv²/2
∴(12g-2g)×2 = v²
∴v² = 20g
∴v = 14m/s.
Again conserving energy at points B and C.
Total energy at B = 2mg + m(14)²/2
Total energy at C = 4mg + mv²/2
∴2mg + m(14²)/2 = 4mg + mv²/2
Solving this you get,
v = 12.52 m/s.
Therefore, speed of roller coaster at point C is 12.52 m/s.
2. The object's volume.
3. The density of the liquid.
Remember what the buoyant force is. It's the lifting force caused by the displacement of a fluid. I'm using the word fluid because it can be either a liquid or gas. For instance a helium balloon floats due to the buoyant force exceeding the mass of the balloon. So let's look at the options and see what's correct.
1. Object's mass
* This doesn't affect the buoyant force directly. It can have an effect if the object's mass is lower than the buoyant force being exerted. Think of a boat as an example. The boat is floating on the top of the water. If cargo is loaded into the boat, the boat sinks further into the water until the increased buoyant force matches the increased mass of the boat. But if the density of the object exceeds the density of the fluid, then increasing the mass of the object will not affect the buoyant force. So this is a bad choice.
2. The object's volume.
* Yes, this directly affects the buoyant force. So this is a good choice.
3. The density of the liquid.
* Yes, this directly affects the buoyant force. You can drop a piece of iron into water and it will sink. You could also drop that same piece of iron into mercury and it will float. The reason is that mercury has a much higher density than water. So this is a good choice.
4. Mass of the liquid
* No. Do not mistake mass for density. As a mental exercise, imagine the buoyant force on a small piece of metal dropped into a swimming pool. Now imagine the buoyant force on that same piece of metal dropped into a lake. In both cases, the buoyant force is the same, yet the lake has a far greater mass of water than the swimming pool. So this is a bad choice.
Answer:
15km/h East (15m/s East option)
Explanation:
Velocity = (change in) Distance/(change in) Time
The distance here is 60km, and the time is 4h, as given by the question. Therefore the velocity is 60km/4h = 15km/h.
To convert km/h to m/s, we just divide the value by 3.6, 15/3.6= 4.17m/s (2dp), which isn't actually an option here, so I'm assuming maybe a mistake in unit for the question?
'Velocity' is a vector quantity, meaning it has a size<em> </em>and a direction, as opposed to speed, a scalar quantity, which only has size. Therefore we need to add a direction for it to be velocity. The given direction here is east, so the velocity of the car is 15km/h East. (I would choose the 15m/s East as the question likely has a unit error and is closest.)
Hope this helped!
Some words that have changed meaning due to technological advances are dial, type, tweet, drone, and spam.
