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2. A ball is thrown from a point 1.00 m above the ground with an initial velocit

ID: 1778543 • Letter: 2

Question

2. A ball is thrown from a point 1.00 m above the ground with an initial velocity 19.6 mls at an angle of 30.00 above the horizontal. a. What is the maximum height (above the ground) that the ball reaches? b. What is the velocity (magnitude and direction) of the ball when it is at this maximum height? c How much time elapses from when the ball is thrown to when it returns to 1.00 m above the ground? What is the velocity (magnitude and direction) of the ball when it returns to 1.00 m above the ground?

Explanation / Answer


initial velocity vo = 19.6 m/s

along vertical


initial velocity voy = vo*sintheta = 19.6*sin30 = 9.8 m/s

acceleration ay = -g = -9.8 m/s^2


initial position y0 = 1 m


at the maximum height final velocity vy = 0

final position y = h


displacement = y - y0 = h - 1

vy^2 - voy^2 = 2*ay*(y-y0)

0 - 9.8^2 = -2*9.8*(h-1)

maximum height = h = 5.9 m <<<---ANSWER


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(b)

at the maximum height


along vertical vy = 0


along horizontal

acceleration ax = o

vx = vox + ax*t


vx = vox = vo*costheta = 19.6*cos30 = 16.9 m/s


at the maximum height velocity v = sqrt(vx^2+vy^2) = 16.9 m/s

direction = along horizontal


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c)

along vertical

initial position y0 = 1 m

final position y = 1 m

initial velcoity voy = 9.8 m/s^2


y - y0 = v0y*t + (1/2)*ay*t^2

0 = 9.8*t - (1/2)*9.8*t^2

t = 2 s

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(d)

along horizontal


acceleration ax = 0


velocity remains same at all times


vx = vox = 16.9 m/s


along vertical

vy = voy + ay*t

vy = 9.8 - (9.8*2) = -9.8 m/s

magnitude = sqrt(vx^2+vy^2) = 19.6 m/s

direction tan^-1(vy/vx) = 30 degrees below the horizontal