hop high . spe tal. clear cross major-league baseball, thrown by Tim Lin- cecum

Question

hop high . spe tal. clear cross major-league baseball, thrown by Tim Lin- cecum in 2009, was clocked at 101.0 mi/h (Fig. P3.22). If a pitch were thrown horizon- tally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 ft away? 28. GP from ity of tal. I of th dinat the i tive x x- and equat as fun Figure P3.22 Tim Lincecum throws a baseball. 23. GP A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach as shown in Figure P3.23. (a) What are the coor- dinates of the initial position of the stone? (b) What are the components of the initial velocity? (c) Write

Explanation / Answer

Here,

height of cliff , h = 50 m

initial speed , u = 18 m/s

a) for the initial position

x0 = 0 m

y0 = 50 m

b)

for the initial velocity

v0x = 18 m/s

v0y = 0 m/s

c) as the horizontal velocity will be constant at all times

vx = 18 m/s

for the vertical velocity

vy = - gt

vy = -9.8 * t

d)

for the position

x = 18t

y = 50 - 0.50 * 9.8 * t^2

y = 50 - 4.9 * t^2

e)

let the time taken is t

as y = 0 = 50 - 4.9 * t^2

t = 3.19 s

the time taken is 3.19 s

f)

for the speed of impact v

v^2 - 18^2 = 2 * 9.8 * 50

solving for v

v = 36.1 m/s

the final speed of impact is 36.1 m/s

for the angle

36.1 * cos(theta) = 18

theta = 60 degree

the angle of impact is 60 degree below horizontal

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