C) Lautaro y Facundo cuentan sus figuritas. Lautaro tiene el doble de las que tiene Facundo menos 3. Si entre los dos tienen 24

figuritas. ¿Cuántas tiene cada uno?

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A child rides a pony on a circular track whose radius is 5.25 m. a) Find the distance traveled and the displacement after the ch

tester [12383]

Answer:

a) The distance covered halfway = 16.49 [m], while the displacement at that point = 10.5 [m]b)

The distance traveled increases

when the child finishes one lap around the track.

Step-by-step explanation:

Distance is a scalar measurement

that indicates how much ground an object has traversed in motion. Contrarily, displacement is a vector measurement which describes how far an object is from its original position after moving.

In this scenario, the child travels halfway around the circular track from point 1 to point 2. We know that the circumference or perimeter of a circle can be calculated as 2*PI*radius. Since the child only covers half the distance, we need to divide the circumference by 2, leading to distance = PI*radius

The halfway distance = (PI)*(5.25) = 16.49 [m]

Considering the definition of displacement, it’s clear that the distance from point 1 to point 2 equals one diameter from the starting point:

The halfway displacement = D = 2*radius = 2(5.25) = 10.5 [m]

b) What occurs to the distance after the child completes one full circuit? The distance will increase since the child covers more ground during the full lap:

The distance for one circuit = 2*(PI)*radius = 2(PI)(5.25) = 32.99 [m]

32.99 is greater than 16.49, confirming that the distance does indeed increase.

3 0

2 months ago

Sanjit drives the 45 km distance between York and Leeds he then drives a further 42 km from Leeds to Blackpool

Leona [12618]

The average speed for his entire journey from York to Blackpool is about 61.41 km/h.

Here’s a breakdown of how we arrive at this:

$\text{ The average speed}=\frac{\text{Total distance covered}}{\text{Total time taken}}$

The distance he travelled from York to Leeds is 45 km,

and the speed during that section was 54 km/h.

Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).

Next, the distance from Leeds to Blackpool is 42 km,

and the time for that leg of the journey is 35 minutes, which is 35/60 hours.

This leads to the total duration for his trip as

$=\frac{45}{54}+\frac{35}{60}=\frac{450+315}{540}=\frac{765}{540}=\frac{17}{12}$ hours.

The cumulative distance covered equals 45 + 42 = 87 km.

Thus, his average speed is calculated as:

$=\frac{87}{17/12}= \frac{12\times 87}{17}=\frac{1044}{17}=61.4117647\approx 61.41\text{ km per hour}$

3 0

3 months ago

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