Tuesday

July 29, 2014

July 29, 2014

Total # Posts: 8,916

**Physics**

Work = Fap*cosA * d=74.1*cos32.3 * 72.4 = 4535 J.

**physics**

V = Vo + a*t. Vo = Initial velocity.

**ap physics**

See previous post: Fri,6-20-14,11:33PM.

**ap physics**

d = d2-d1 = 120m[105o]-60m[15o] X = 120*cos105 - 60*cos15 = -89.0 m. Y = 120*sin105 - 60*sin15 = 100.4 m. Tan Ar = Y/X = 100.4/-89.0 = -1.12789 Ar = -48.44o = Reference angle. A = -48.44 + 180 = 131.6o = Direction. d = Y/sinA = 100.4/sin131.6 = 134.3 m. [131.6].

**math**

a ball is thrown down ward from a 320 ft building at a initial velocity of 32 ft per sec. How long would the ball take to reach a height of 48 feet?' 16t^2+32+320

**Please help! Urgent**

Po =(1-0.08) * 8500 = $7820. P = 243.07/mo. * 36mo. = $8750.52 P = Po + Po*r*t = 8750.52 7820 + 7820*r*3 = 8750.52 7820 + 23,460r = 8750.52 23,460r = 8750.52-7820 = 930.52 r = 3.97% or 4.0% = APR.

**Survey of mathematics**

Solved under a later post.

**Survey of Mathematics**

Correction: 100%-5% = 95% borrowed.

**Survey of Mathematics**

100% - 5% = 95% Down payment. Po = 0.95 * $289,000 = $274,550.=Amount of loan. P = (Po*r*t)/(1-(1+r)^-t) r = (6%/12)/100% = 0.005=Monthly % rate. t = 25yrs. * 12mo./yr. = 300 months. Plug the above values into the given Eq and get: P = $530,678.85 = Total cost of the house. 2 ...

**Survey of mathematics**

Po = P - 0.08P = 8500-(0.08*8500)= $7820 243.07/mo. * 36mo. = $8750.52 Paid back. I = Po*r*t = 8750.52-7820.00 = 930.52 7820*r*3yrs. = 930.52 23460r = 930.52 r = 0.0397 = 3.97% = APR.

**physics**

Vp+Vw = 275km[45o] Vp + 55km[90o] = 275[45o] Vp + 55i = 275*cos45 + i275sin45 Vp + 55i = 194.45 + 194.45i Vp = 194.45 + 194.45i - 55i Vp = 194.45 + 139.45i = 239.3km[35.6o] = Velocity and heading of plane. Check: 194.45+139.45i + 55i = 194.45 + 194.45i = 275[45o]

**trig**

V(0,0), T(-12,5) X = -12 - 0 = -12. Y = 5- 0 = 5. r = Sqrt(X^2+Y^2) = Sqrt(144+25) = 13 Sin A = Y/r = 5/13. Cos A = X/r = Tan A = Y/X CSC A = r/Y Sec A = Cot A = NOTES: V = Vertex. T = Terminal side. Sqrt = Square root.

**Algebra**

(2b-2)/(2b^2-8) 2b^2-8 = 0 2b^2 = 8 b^2 = 4 b=+-2 Gives a denominator of zero which makes the expression Undefined. Domain: All real values of b except +2 and -2. Mathematically: -2 > b > 2.

**Physics**

1. See previous post:Tue,6-17-14,9:52 PM 2. Xo = 4.0 m/s. h = 0.5g*t^2 = 6.5 m. 4.9*t^2 = 6.5 t^2 = 1.327 Tf = 1.15 s. = Fall time. d = Xo * Tf = 4.0m/s * 1.15s = 4.60 m.

**Physics**

Glad I could help.

**Physics**

1. r1=d/t = 30m/5s = 6 m/s.=Speed of rabbit r2=30m/120s = 0.25 m/s.=Speed of turtle T1 = d/r1 = 96/6 = 16 s.=Rabbit's time. T2 = d/r2 = 96/0.25 = 384 s. = Turtle's time. T2 - T1 = 384 - 16 = 368 s. 2. T2 = d/r2 = 500/10 = 50 s. = Time of red bicycle. d = r1 * T1 = 500 ...

**math**

Incomplete.

**Physics**

T1 = d1/r1 = 800/6 = 133.3 s. T2 = d2/r2 = 800/8 = 100 s. a. T1+T2 = 133.3 + 100 = 233.3 s.=Total time of travel. b. r = d/T = 1600m/233.3s = 6.86 m/s.

**Physics**

Direction = 25.0o West of north? a. D = 290m[25.0o] t = D/V = 290[25.0]/2[25o] = 145 s. b. r = D/t = 290m/145s = 2m/s.

**physics**

d1 + d2 = 4-1 = 3 m. (0.5g*t^2) + (Vo*t+0.5g*t^2) = 3 m. 4.9t^2 + 6t+(-4.9t^2) = 3 6t = 3 t = 0.5 s. d1 = ho - 0.5g*t^2 d1 = 4 - 4.9*0.5^2 = 4 - 1.225=2.775 m. Above gnd. d2 = 1 + (6*0.5 + (-4.9)*0.5^2 d2 = 1 + (3 + (-1.225) = 1 + 1.775=2.775 m. Above gnd. Therefore, the ball ...

**Angles,Lines and Triangles**

A1 = A2 Eq: A1 + A2 + A3 = 180o A1 + A2 + (A1+18) = 180 Replace A2 with A1: A1 + A1 + (A1+18) = 180 3A1 + 18 = 180 3A1 = 180-18 = 162 A1 = A2 = 54o A3 = A1 + 18 = 54 + 18 = 72o.

**math apr**

See previous post: Tue,6-10-14, 10:55AM.

**math**

Jerry's number = n. Mike's number = n+2000 Barry's number = n+400. Larry's number = 443+1500 = 1943. Sam'2 number = 443. Barry's number = 443+60 = 503. n+400 = 503 n = 103 n+2000 = 103+2000 = 2103

**Physics**

Fg=m*g = (66.2kg+5.3kg)*9.8N/kg=700.7 N. = Force of gravity = Combined wt. of person and sled. Ff = u*Fg = 0.12 * 700.7 = 84.1 N. = Force of friction. Fx-Ff = m*a Fx-84.1 = m*0 = 0 Fx = 84.1 N.

**math**

Y = 1.5x X = The # of bottles of water purchased. Y = Total cost in dollars. (x,y) (1,1.5) (2,3) (3,4.5) (4,6).

**Physics**

r = 225km/h = 225000/3600s = 62.5 m/s. = Average speed for full length. r1 = 205km/h = 205000m/3600s = 56.94 m/s.= Average speed for 1st half(700m). (r1+r2)/2 = r (56.94+r2)/2 = 62.5 m/s. 56.94 + r2 = 125 r2 = 125-56.94 = 68.06 m/s = Average speed for 2nd half of race.

**Physics**

Johnny: T1 = 4 min,57s = 240+57 = 297 s. Martha: T2 = 4 min,38s = 240+38 = 278 s. r2 = 400m/278s. = 1.439 m/s. d = r2*(T1-T2) = 1.439(297-278)=27.3 m.

**algebra**

Sum = 8 = 7+1 = 6+2 = 5+3 = 4+4 Select 5, and 3: Original #: 53. Reversed: 35. Difference = 53-35 = 18.

**algebra**

X Nickels. (16-X) Qtrs. 5x + 25(16-X) = 220 Cents. Solve for X.

**Algebra 2**

S1+S2+S3 = 5 Ft. S1 = S2 = S3 S1+S1+S1 = 5 3S1 = 5 S1 = 5/3 Ft. = 20 In. = S2 = S3. (s/2)^2 + h^2 = S^2 (20/2)^2 + h^2 = 20^2. Solve for h.

**Algebra 2**

N Large packages. (12-N) Small packages. Cost = 7n + 4.5(12-n) Cost = 7n + 54-4.5n = 2.5n + 54.

**physics**

h = 0.5g*t^2 = 1 m. 4.9t^2 = 1 t^2 = 0.204 t = o.452 s. = Fall time. d = Vo*t = 1.32 m. Vo*0.452 = 1.32 Vo = 2.92 m/s.

**physics**

V = 42.3mi/40min * 1600m/mi * 1min/60s = 28.2 m/s. V = 42.3mi/40min * 1.6km/mi * 60min/h = 101.5 km/h.

**physics**

V = 22.7[32o] Momentum=m*V = 537 * 22.7=12,190 kg-m/s.

**Physics**

Wt. = 1.8 Tonne. Vo = 3 m/s. d = 45 m. Fk = 80 N. Mass = 1.8 * 1000kg = 1800 kg. Fg = m*g = 1800 * 9.8 = 17,640 N. KE + PE = mg*h-Fk*d KE + PE = mg*h-80*45 0.5m*Vo^2 + 0 = mg*h-3600 900*9 + 3600 = 17640h 17,640h = 11,700 h = 0.6633 m. sinA = h/d = 0.6633/45 = 0.01474 A = 0.84o...

**physics**

99. If you drop an object: Vo = 0 = Initial velocity. a = g = 10 m/s^2. If you throw it down: Vo > 0 a = g = 10 m/s^2. So in both cases, the acceleration remains constant at 10 m/s^2.

**Algebra**

6x-72 = 0 6x = 72 X = 12

**Math**

y-6=> 12 Y =>12+6 Y => 18 This is the Eq of a hor. line in which Y => 18 for all values of X.

**calculus**

V = Vo + a*t = 2000 + (-3000)*0.03 = 1910 m/s.

**physics**

Momentum = m*V = 5 * 3 = 15 kg-rad/s.

**Algebra 1**

1.(15-5x)/(x^2-9x+18). -5(x-3)/(x-3)(x-6) = -5/(x-6). 2. T=T1*T2/(T1+T2) T = 40*60/(40+60)=24 min. 3. A*C = 2*(-20)-40 = 4*(-10) = 5*(-8) B = The sum of the pair of factors that are divisible by 2: B = 2+(-20) = -18 B = 4+(-10) = -6 Eq1: 2x^2-18x-20 = 0 Divide by 2: x^2-9x-10...

**Physics**

a. V=110km/h = 110000m/3600s.=30.56 m/s V^2 = Vo^2 + 2g*h h = (V^2-Vo^2)/2g = (0-(30.56)^2/-19.6 = 47.6 m.

**Physics**

d = (24.5N./2500N.)*1M = = 0.0098 M.

**math - APR**

a. (42,650-5100)/60 = %625.83/mo. b. P = (Po*r*t)/(1-(1+r)^-t) Po = 42,650-5100 = 37550 r = (2.5%/12)/100% = 0.00208 t = 60 Months. Plug the above values into the given Eq and get: P = $39,984.81 39984.81/60mo = $666.41/mo. = Monthly payments. c. I = (39984.81-37550)/5yrs = $4...

**math**

Use synthetic(long-hand) division: (2x^3-5x^2+x+2)/(x-2) = 2x^2-x-1 a = 2, and b = -1.

**physics**

Green = 0.99*200 = 198 White = 0.01*200 = 2 X green marbles removed. (200-x) Marbles remaining. 0.98(200-x) + 2 = 200-x 196-.98x + 2 = 200-x 0.02x = 200-198 = 2 X = 100 Green marbles removed. 198-100 = 98 Green marbles remaining. 200-100 = 100 total Marbles remaining. Check: G...

**Physics**

a. Fb = m*g = 76 * 9.8 = 744.8 N. = Force of barbell. Po = 20 * 744.8 * 2.6/90s = 430.3 J/s = 430.3 W. b. hp = 430.3/746 = 0.577

**physics**

See previous post.

**physics**

V^2 = Vo^2 + 2g*h = 0 + 20*10 = 200 V = 14.14 m/s. 0.5g*t^2 = 10 m. 5t^2 = 10 t^2 = 2 t = 1.414 s.

**physics**

Vo = 136km/h = 136,000m/3600s=37.78 m/s V^2 = Vo^2 + 2a*d d = (V^2-Vo^2)/2a d = (0-(37.78^2))/-500 = 2.85 m.

**Math Personal Finance**

See previous post.

**Math Personal Finance**

P = Po(1+r)^n = 2000 r = (6%/12)/100% = 0.005 n = 12comp/yr. * 5yrs. = 60 compounding periods. Po(1.005)^60 = 2000 Po = 2000/(1.005^60) = $1482.74=Initial deposit or present value.

**Math Personal Finance**

P=Po(1+r)^n. Calculate int. for 1 year. r = (5%/12)/100% = 0.00417 = Monthly % rate expressed as a decimal. n = 12comp./yr. * 1yr. = 12 Compounding periods. P = 7000(1.00417)^12 = $7358.13 I = P-Po = 7358.13 - 7000 = $358.13 APY = (I/Po)*100% = (358.13/7000)*100% = 5.116%

**Engg Mechanics**

Block A: 200*sin30 = 100 N. = Force parallel to the plane. Fn = 200*cos30 = 173.2 N. = Normal force Block B: 100*sin30 = 50 N. = Force parallel to the plane. Fn = 100*cos30 = 86.6 N. = Normal force. P = Wa+Wb = 200 + 100 = 300 N.

**electronics**

Given: i = 6 mA. t = ? 1. Locate 6 mA on the y-axis. 2. Draw a hor. line from 6 mA to the curve. 3. Draw a ver. line from the intersection of the hor. line and curve to the x-axis. 4.Read the time, t , at the intersection of the ver. line and x-axis. Note: When t is given, dra...

**physics**

a. The force of static friction decreases. b. The force of friction increases. The max. possible value of the force of friction increases. The max. angle at which block will slide decreases.

**Physics**

Upward: a = g = -9.8 m/s^2(slowing down) Highest point: a = g = -9.8 m/s^2. Downward: a = g = 9.8 m/s^2. The data shows that the acceleration due to gravity is present during the entire flight of the object. If g goes to zero, the object would not come down.

**Physics**

a. V^2 = Vo^2 + 2g*d V^2 = 4.9^2 + 19.6*21 = 435.61 V = 20.87 m/s. b. V = Vo + g*t t = (V-Vo)/g = (20.87-4.9)/9.8 = 1.63 s.

**physics**

a. False.

**Science**

2. Slower object: KE = 0.5m*V^2. Faster object: KE = 0.5m*(2V)^2 = 0.5m*4*V^2. 0.5m*4V^2/0.5m*V^2 = 4 Times. 3. KE = 0.5m*V^2 9. MA = 20/100 10. W = F*d. d = 0.

**Physics**

a. Vo=36mi/h * 1600m/mi * 1h/3600s=16 m/s. V^2 = Vo^2 + 2a*d d = (V^2-Vo^2)/2a d = (0-256)/-10 = 25.6 m. b. d = 0-1024)/-10 = 102.4 m.

**MULTIPLY. WRITE EACH PRODUCT IN SCIENTIFIC NOTATIO**

post.

**MULTIPLY. WRITE EACH PRODUCT IN SCIENTIFIC NOTATIO**

24. (3*10^6)(2*10^12) = 6*10^(6+12)=6*10^18 26. (6*10^9)(5*10^4) = 30*10^(9+4) = 30*10^13 = 3*10^14

**MULTIPLY. WRITE EACH PRODUCT IN SCIENTIFIC NOTATIO**

34. 5^10/5^7 = 5^(10-7) = 5^3 36. 76^11/76^5 = 76^(11-5) = 76^6

**electronics**

Rt = R2*R3/R1 = 2.11k R2*8.2k/2.2k = 2.11k 3.727R2 = 2.11k R2 = 0.566k = 566 ohms. NOTE: I'm assuming that Rt = 2.11k at 0oC.

**physics**

Yes, when an object is DROPPED, the initial velocity is 0. When an object is THROWN up or down, the initial velocity is not 0. V^2 = Vo^2 + 2g*h V^2 = 0 + 19.6*7 = 137.2 V = 11.71 m/s.

**Math**

1. ) = 30 + 0.1(x-200) F(x) = 30 + 0.1x - 20 The above Eq is valid for all real values of X that are equal to or greater than 200: X => 200. When x = 200 minutes, the cost would be $30. None of the given choices meets this requirement. 2. Cost = 30 + 0.1x - 20 = $100 0.1x =...

**math**

See previous post: Fri,5-23-14,12:35 PM.

**electrical circuit instrumentation**

R1 = 6 ohms. R2 = 8 ohms. Re=R1*R2/(R1+R2) = 6*8/(6+8)=3.429 ohms = Equivalent resistor. I1 = E/R1 = 36/6 = 6 Amps. I2 = E/R2 = 36/8 = 4.5 Amps. I = I1+I2 = 6 + 4.5 = 10.5 Amps. P1 = E^2/R1 = 36^2/6 = 216 Watts. P2 = E^2/8 = 36^2/8 = 162 Watts. P = P1+P2 = 216 + 162 = 378 Watt...

**mechanical physics**

Incomplete.

**Physics**

1. h = 0.5g*t^2 = 6 m. 4.9t^2 = 6 t^2 = 1.224 Tf = 1.107 s. = Fall time. d = Xo * Tf = 24 m. Xo * 1.107 = 24 Xo = 21.7 m/s = Initial velocity. 2. Fg = m*g = Force of gravity = Wt. of car. Fk = u*Fg = Force of kinetic friction. Fn = Fap-Fk = Net force. Fap = Force applied.

**science**

1. V = Vo + g*t = 30 - 10*2 = 10 m/s. 2. hmax = (V^2-Vo^2)/2g hmax = (0-(30)^2)/-20 = 3. V = Vo + g*Tr = 0 @ hmax. Tr = -Vo/g = -30/-10 = 3 s. = Rise time.

**math**

I=2.37*10^-5 watts/cm^2=Sound Intensity level. Io =10^-16 W/cm^2 = Reference sound Intensity level. db = 10*Log(I/Io) db = 10*Log(2.37*10^-5/10^-16) = 114

**physics**

Fx = 100*Cos37 = 79.86 N. Wb = m*g = 10kg * 9.8N/kg = 98 N. = Weight of buggy. a=(Fx-Fk)/m = (79.86-60)/10=1.99 m/s^2

**physics**

d1 = d2 25t = 0.5a*t^2 25 = 0.5a*t 0.002t = 25 t = 12,500 s. = 3.5 h.

**physics**

d = 300km[135o] V1 = 300km[135o]/0.75h = 400 km/h[135o] without wind. Vp + Vw = 400o[135] Vp + 80[-90o] = 400[135] Vp = 400[135] - 80[-90] Vp=400*cos135+i400*sin135 - (80*Cos(-90)+i80*sin(-90)) Vp = -282.84+i282.84 - (0-i80) Vp = -282.84 + i362.84 = 460km[128o] = Velocity and ...

**Algebra 1 (Reiny)**

1. T = T1*T2/(T1+T2) = 2*3/(2+3)=1.2 h. 2. H = 0.4 * 300 = 120 mL in current solution. W = 0.6 * 300 = 180 mL of water in current solution. W/(W+H) = 0.7 W/(W+120) = 0.7 W = 0.7W + 84 0.3W = 84 W = 280 mL of water in new solution. 280-180 = 100 mL of water added to new solution.

**geometry**

A1 = 150o = Minor Arc. A2 = 360-150 = 210o = Major Arc. X = (A2-A1)/2 = (210-150)/2 = 30o=Angle formed by 2 tangents. a

**College Algebra**

Length = L units. Width = (2L-2) units. A = L(2L-2) = 82cm^2 2L^2 - 2L - 82 = 0 L^2 - L - 41 = 0 Use Quadratic formula: L = 6.92 cm. Width = 2L - 2 = 2*6.92 - 2 = 11.84 cm. The diagonal divides the rectangle into 2 congruent rt. triangles. D^2 = L^2 + W^2 = 6.92^2 + 11.84^2=18...

**College Algebra ..Please help**

1. Width = W ft. Length = (W+20) ft. A = W*(W+20) = 8,000 Ft^2 W^2 + 20W - 8000 = 0 C=-8,000 = -80*100. Sum = -80+100=20=B. (w+100)(w-80) = 0 w+100 = 0, W = -100 w-80 = 0, W = 80 Ft = Width. w+20 = 80+20 = 100 Ft = Length. 2. A = L*W = 16, L = 16/W. Eq2: L^2 + W^2 = 68 In Eq2,...

**LOOK AT THE GIVEN TRIANGLES??**

a. P1 = (4x+2) + (7x+7) + (5x-4)=16x + 5 P2 = (x+3) + (x+7) + (2x-5) = 4x+5 b. P1-P2 = (16x+5) - (4x+5) = 16x+5 - 4x-5 = 12x.

**physics**

d = 3.6 + 0.5 = 4.1 miles. T1 = 3.6/9 + 12/60 = 0.6 hr. To travel 4.1 miles from starting point. V1 = d/T1 = 4.1/0.6 = 6.83 mi/h. V2=9.0 mi/h. when returning to starting point. V = (V1+V2)/2 = (6.83+9.0)/2 = 7.92 mi/h = Average velocity for entire trip.

**physics**

T^2 = 4pi^2(L/g) = 3.4^2 39.48(2.87/g) = 11.56 113.3/g = 11.56 11.56g = 113.3 g = 9.80 m/s^2

**Kirr**

P = Po(1+r)^n = $25,000 r = (1.825%/365)/100% = 5*10^-5 = Daily % rate expressed as a decimal. n = 365Comp./yr. * 4yrs. = 1460 Compounding periods. Po(1.00005)^1460 = 25000 Po = 25,000/1.00005^1460 = $23,240.

**algebra math!**

9pts/6wks = 1.5 Points/week.

**physics**

Wb = m*g = 40kg * 9.8N/kg = 392 N. = Weight of box. Fk=u*(Wb-F*sin31)=0.45(392-173*sin31) = 136.3 N.= Force of kinetic friction. Fn=F*CosA-Fk = 173*cos31 - 136.3 = 12 N. = Net force. a = Fn/m = 12/40 = 0.30 m/s^2.

**Physics**

hmax = L*sin A = 5*sin40 = 3.21 m. At top of incline: KE + PE = mg*hmax-Fk*L 0 + PE = mg*3.21-10*5 PE = mg*3.21-50. At bottom of incline: KE + PE = mg*3.21-50 KE + 0 = mg*3.21-50 KE = mg*3.21-50 = 35 J. m*9.8*3.21-50 = 35 31.5m-50 = 35 31.5m = 85 m = 2.7 kg. = Mass of box.

**physics**

V = Vo + g*Tr = 0 at max. ht. Tr = -Vo/g = -40/-9.8 = 4.08 s. = Rise time. T = 4.08-1 = 3.08 s. h1 = Vo*t + 0.5g*t^2 h1 = 40*3.08 - 4.9*3.08^2 = 76.7 m. h2 = 40*4.08 - 4.9*4.08^2 = 81.6 m. h2-h1 = 81.6-76.7 = 4.93 m. = Distance traveled in the last second.

**physics**

h = Vo*t + 0.5g*t^2 h = 0 + 5*3^2 = 45 m. = Height of object above gnd. (45-1)/4m = 11th floor.

**physics**

V^2 = Vo^2 + 2a*d V^2 = 0 + 10*10 = 100 V = 10 m/s.

**algebra**

I = 2.42*10^-5 Watts/cm^2. = Sound intensity. Io = 10^-16 Watts/cm^2 = Reference sound intensity. dB = 10^Log(2.42*10^-5/10^-16) = 114.

**physics**

h = L*sin A = 5.5*sin30 = 2.75 m. Fn = mg*Cos A = 66*Cos 30 = 57.16 N. = Normal force = Force perpendicular to the ramp. Fk = u*Fn = 0.22 * 57.16 = 12.57 N. = Force of kinetic friction. KE + PE = mg*hmax-Fk*L KE + PE = 66*2.75-12.57*5.5 = 112.4 J. 0 + PE = 112.4 PE = 112.4 J. ...

**physics**

1. W = Fk*d 25 * 12 Joules. 2. W = 175 * 12 Joules. 3. Wn = (175*12)-(25*12)

**Physics**

a. X = 45 N. Y = -22 N. F^2 = 45^2 + (-22)^2 = 2,509 F = 50.09 N. b. d = 22m/s * 3s = 66 m. Work = F*d = 50.09 * 66 = 3306 Joules.

**Physics! Help**

F1 + F2 = 96.2N.[55.4o] + 11.6N.[41.2o] X = 96.2*cos55.4 + 11.6*cos41.2=63.35 N

**ALGERBRA**

What are the "2 ways?" Perhaps some punctuation would help.

**Physics**

F = m*a = 1350 N. Impulse=m*V = m*(a*T) = 1350*6.2*10^-3= 8.37 kg-m/s.

**Physics**

D=2m[270o] + 16m[180o] + 24m[90o]+36m[180o]. Add the two 180o vectors directly: D = 2[270o] + 52[180o] + 24[90o] X = 2*cos270+52*cos180+24*cos90 = -52 m. Y = 2*sin270+52*sin180+24*sin90 = 22 m. D^2 = (-52)^2 + 22^2 = 3188 D = 56.5 m.

**Physics**

a. d = V*T = 420 m. (12.5-2.70) * T1 = 420 T1 = 420/(12.5-2.70) = 42.9 s. b. T2 = 420/(12.5+2.7) = 27.6 s. T = T1+T2 = 42.9 + 27.6 = 70.5 s. c. T1 = 420/12.5 = 33.6 s. T2 = T1 = 33.6 s. T = 33.6 + 33.6 = 67.2 s.

**physics**

V=100mi/h * 1600m/mi * 1h/3600s = 44.44m/s V = Vo + a*t = 0 a = -Vo/t = -44.444/10^-3=-44,444 m/s^2 F = m*a = 0.145 * (-44,444) = - 6444 N.

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