Question

Help me answer thiscant understand even my teacher give clue

Answer 1

Answer:

The two particles will meet after 50 seconds

Distance traveled by the first particle = 1225 cm

Distance traveled by the second particle = 625 cm

Step-by-step explanation:

For the first partiicle

The sequence representing the distance traveled after every 2 seconds is:

97, 93, 89, .........

The common difference, d = 93 - 97 = 89 - 93

d = -4

The distance traveled in the first two seconds, a = 97

Let the number of terms be n

This is an arithmetic sequence, and the distance traveled after n 2 seconds will be:

`\begin{gathered} T_n=\text{ a + (n-1)d} \\ T_n=\text{ 97 + (n-1)(-4)} \\ T_n=\text{ 97-4n+4} \\ T_n=\text{ 101-4n} \end{gathered}`

For the second particle

The sequence representing the distance traveled every 2 seconds is:

49, 47, 45,......

The common difference, d = 47-49 = 45 - 47 = -2

d = -2

The distance traveled in the first two seconds is a = 49

The nth term of the sequence is:

`\begin{gathered} T_n=\text{ a + (n-1)d} \\ T_n=49+(n-1)(-2) \\ T_n=\text{ 49-2n+2} \\ T_n=\text{ 51-2n} \end{gathered}`

When the two particles collide, the two equations can be equated

`\begin{gathered} 101-4n\text{ = 51 - 2n} \\ 4n\text{ - 2n = 101-5}1 \\ 2n\text{ = }50 \\ n=(50)/(2) \\ n=25 \end{gathered}`

These two particles will collide after 25 distances, and since each distance takes 2 seconds, the time taken for the particles to meet will be:

t = 2n

t = 2(25)

t = 50

The particles will meet after 50 seconds

Sum of n terms of an Arithmetic Sequence is:

`S_n=\text{ }(n)/(2)\lbrack2a+(n-1)d\rbrack`

For the first particle:

a = 97, d = -4, n = 25

`\begin{gathered} S_(25)=\text{ }(25)/(2)\lbrack2(97)+(25-1)(-4)\rbrack \\ S_(25)=\text{ 12.5(}194-96) \\ S_(25)=\text{ }1225 \end{gathered}`

The distance traveled by the first particle = 1225 cm

For the second particle:

a = 49, d = -2, n = 25

`\begin{gathered} S_(25)=\text{ }(25)/(2)\lbrack2(49)+(25-1)(-2)\rbrack \\ S_(25)=\text{ 12.5(}98-48) \\ S_(25)=12.5(50) \\ S_(25)=\text{ }625 \end{gathered}`

The distance traveled by the second particle = 625 cm