Emmy kicks a soccer ball up at an angle of 45° over a level field. She watches t

Question

Emmy kicks a soccer ball up at an angle of 45° over a level field. She watches the bal's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. Assume that air resistance is ligable, and plot the horizontal and vertical components of the ball's velocity as a function of time. Consider only the time that the ball is in the air, after being kicked but before landing. Take "north" and "up" as the positive x and y directions, respectively, and use g 10 m/s2 for the downward acceleration due to gravity. Vx Im/s]Horizontal Velocity 15 vy Im/sVertical Velocity 15 10 10 10 -10 ts5 tIs) -15 0.5 1.5 0.5 1.5 2

Explanation / Answer

The center to center distance is:

R = 285 x 10^6 + 3.6 x 10^6 = 288.6 x 10^6

The distance moon has to cover is equal to the circumferenec of the circle

D = 2 pi R

D = 2 x 3.14 x 288.6 x 10^6 = 1.812 x 10^9 m

speed = d/t

v = 1.81 x 10^9/1.46 x 10^6 = 1.241 x 10^3 m/s

we know that, radial acceleration is given by:

a = v^2/R

a = (1.241 x 10^3)^2/288.6 x 10^9 = 5.34 x 10^-3 m/s^2

Hence, a = 5.34 x 10^-3 m/s^2

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