A turtle can run at a speed of 10 cm/s. and a rabbit can run 20 times as fast. I

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A turtle can run at a speed of 10 cm/s. and a rabbit can run 20 times as fast. In a race, they both start at the same time, but the rabbit stops to rest for 1 minutes If the turtle and the rabbit cross the finish line at exactly the same time, what was the distance of the race? A car traveling along a straight road increases its speed from 30 m/s to 50 m/s over a distance of 180 m. If the acceleration is constant, how much time elapses while the car moves this distance? An airplane flies directly North at a speed of 150 km/h with respect to the air. If the air then moves with a velocity of 60 km/h, 10 degree South of East, what is the total speed of the airplane with respect to the ground? A stone is thrown with a velocity of 21 m/s at an angle of 50 degree above the horizontal. If the stone is traveling horizontally when it hits a window, what is the horizontal distance of the building from the thrower of the stone? A 2 kg block and a 4 kg block are up against each other on a horizontal frictionless surface. The 2 kg block is pushed with a horizontal force of 12 N toward the 4 kg block, while the 4 kg block is pushed with a horizontal force of 30 N toward the 2 kg block. What is the magnitude of the force that each block exerts on the other? A force acting upwards and parallel to a frictionless 36 degree incline pulls an 8 kg mass at a constant velocity. What is the magnitude of that force? In a game of shuffleboard (where disks are given an initial push and then slide freely on a horizontal surface), a disk is given an initial speed of 6 m/s. It travels a distance of 9 m before coming to rest. What is the coefficient of kinetic friction between the disk and the surface? What is the highest velocity at which a car can drive over the top of a hill of radius 55 m without leaving the ground? Suppose a faraway moon belonging to another planet has the same mass as our moon, but 1.4 times the radius. What is the free fall acceleration on the surface of that moon? Our moon has a free fall acceleration of 1.6 m/s2. A satellite circles a planet every 2.8 hours in a circular orbit having a radius of 1.2 times 107 m. What is the mass of the planet?

Explanation / Answer

1) let t is the time taken

v_T*t = v_R*(t-60)

v_T*t = 20*v_T*(t-60)

t = 20*(t-60)

t = 20*t - 1200

t = 1200/19

= 63.16 s

d = v_T*t

= 10*63.16

= 632 cm

= 63.2 m

2) a = (v^2 - u^2)/2*s

= (50^2-30^2)/(2*180)

= 4.44 m/s^2

t = (v-u)/a

= (50-30)/4.44

= 4.5 s

3)

v(A/G) = sqrt(150^2 + 60^2 + 2*150*60*cos(100))

= 152 km/h

4)

x = R/2 = vo^2*sin^2(2*theta)/(2*g)

= 21^2*sin^2(2*50)/(2*9.8)

= 22 m

5) Fnet = (30-12) = 18 N

a = Fnet/(m1+m2) = 18/(4+2) = 3 m/s^2

F(conatct force) = 12 + m1*a

= 12 + 2*3

= 18 N

6) F = m*g*sin(36)

= 8*9.8*sin(36)

= 46.1 N

7) a = (v^2-u^2)/2(2*s)

= a = (0^2-6^2)/(2*9)

= -2 m/s^2

a = -mue_k*g

-2 = -mue_k*9.8

mue_k = 2/9.8

= 0.204

8) v = sqrt(g*r)

= sqrt(9.8*55)

= 23.2 m/s

9) g' = G*M/R'^2

= G*M/(1.4*R)^2

(1/1.4)^2*(G*M/R^2)

= g/1.4^2

= 1.6/1.4^2

= 0.816 m/s^2

10) T = 2*pi*r/v

v = 2*pi*r/T

= 2*pi*1.2*10^7/(2.8*60*60)

= 7480 m/s

V = sqrt(G*M/r)

==> M = v^2*r/G

= 7480^2*1.2*10^7/(6.6710^-11)

= 1.01*10^25 kg

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