Physics, 22.09.2019 19:30 bella51032

Mary and sally are in a foot race. when mary is 22 m from the finish line, she has a speed of 4.0 m/s and is 5.0 m behind sally, who has a speed of 5.0 m/s. sally thinks she has an easy win and so, during the remaining portion of the race, decelerates at a constant rate of 0.50 m/s2 to the finish line.

Answers: 1

Show answers

Answers

Answer from: davidtrott5761

$0.604 m/s^{2}$

Explanation:

The complete question is:

Mary and Sally are in a foot race (see the figure). When Mary is 22 m from the finish line, she has a speed of4.0 m/s and is 5.0 m behind Sally, who has a speed of5.0 m/s. Sally thinks she has an easy win and so, during the remaining portion of the race, decelerates at a constant rate of 0.44m/s2 to the finish line.

What constant acceleration does Mary now need during the remaining portion of the race, if she wishes to cross the finish line side-by-side with Sally?

We have the following data:

Mary's speed: $V_{M}=4m/s$

Mary's distance to the finish line: $d_{M}=22 m$

Sally's speed: $V_{S}=5m/s$

Sally's distance to the finish line: $d_{S}=22 m- 5 m=17 m$

Sally's acceleration: $a_{S}=-0.44 m/s^{2}$ because we are told she decelerates

We need to find Mary's acceleration: $a_{M}$

But firstly, we have to find the time it takes Sally to reach the finish line, which is the same time Mary will have to reach the finish line. This can be done by the following equation:

$d_{S}=V_{S}t+\frac{1}{2}a_{S}t^{2}$ (1)

Rewritting the equation:

$\frac{1}{2}a_{S}t^{2}+V_{S}t-d_{S}=0$ (2)

$\frac{1}{2}(-0.44 m/s^{2})t^{2}+5m/s t-17m=0$ (3)

Multiplying by 1 each side of the equation:

$(0.22 m/s^{2})t^{2}-5m/s t+17m=0$ (4)

This is a quadratic equation (also called equation of the second degree) of the form $at^{2}+bt+c=0$ , which can be solved with the following formula:

$t=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$ (5)

Where:

a=0.22

b=-5

c=17

Substituting the known values:

$t=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(0.22)(17)}}{2(0.22)}$ (6)

Solving (6) we take the smaller result (because the longer result is equivalent to the time it takes to Sally to reach the finish line, change her direction and cross the finish line again):

t=4.18 s (7) Now that we have the time, we can calulate Mary's acceleration

$d_{M}=V_{M}t+\frac{1}{2}a_{M}t^{2}$ (8)

Isolating $a_{M}$ :

$a_{M}=\frac{2(d_{M}-V_{M}t)}{t^{2}}$ (9)

$a_{M}=\frac{2(22m-(4 m/s)(4.18 s))}{(4.18 s)^{2}}$ (10)

Finally:

$a_{M}=0.604 m/s^{2}$ (11) This is the acceleration Mary needs if she wishes to cross the finish line side-by-side with Sally.

Mary and sally are in a foot race. when mary is 22 m from the finish line, she has a speed of 4.0 m/

Answer from: Quest

answer: i pick a

explanation:

Answer from: Quest

Answer:

the word that best describes martin luther king jr.'s tone in the video is dignified

explanation:

martin luther king, jr. was a social activist and baptist minister who played a key role in the american civil rights movement from the mid-1950s until his assassination in 1968. the video shows his manner and attitude having or showing a composed or serious manner that is worthy of respect so dignified is the correct answer

Another question on Physics

Physics, 22.06.2019 10:20

Asmall object with mass 0.200 kg swings back and forth on the lower end of a light rope that is 3.00 m long. the upper end of the rope is attached to the ceiling. as the object swings through its lowest position, where the rope is vertical, the speed of the object is 5.80 m/s. at this point in the motion, what is the tension in the rope? (use g = 9.80 m/s2.)

Answers: 2

Answer

Physics, 22.06.2019 12:20

What is the coefficient of kinetic friction μk between the block and the tabletop?

Answers: 1

Answer

Physics, 22.06.2019 16:30

Write a polynomial function with the given zeros x= -1,0,2show your work

Answers: 3

Answer

Physics, 22.06.2019 18:00

Acid precipitation chemically weathering a 5.0-kg limestone rock . which coukd be the result ?