The motion diagram below shows a ball\'s position at regular intervals as the ba

Question

The motion diagram below shows a ball's position at regular intervals as the ball flies from left to right through the air. Note that the graph shows the ball's vertical position as a function of its horizontal position. The small squares on the diagram measure 1.00 m by 1.00 m. Use g 10.0 m/s, and neglect air resistance. (a) Calculate the vertical component of the ball's initial velocity. (b) Calculate the total time the ball spends in the air (c) Calculate the horizontal component of the ball's initial velocity m/s (d) Calculate the angle, measured counter-clockwise from the positive x-direction, at which the ball was launched

Explanation / Answer

here,

maximum height , hmax = 16 m

range , R = 16 m

a)

the vertical component of velocity , uy = sqrt(2*g*hmax)

uy = sqrt(2*9.81 * 16) m/s

uy = 17.7 m/s

b)

the time spend in air , t = 2*uy /(g)

t = 2 * 17.7 /9.8 s

t = 3.62 s

c)

the horizontal component of velocity , ux = 16/t = 4.42 m/s

d)

the angle theta = arctan(uy/ux)

theta = 76 degree

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