A baseball player friend of yours wants to determine his pitching speed. You hav

Question

A baseball player friend of yours wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation 7.0 in above the ground. The ball lands 20 m away. What is his pitching speed? Express your answer using two significant figures. Part B As you think about it, you're not sure he threw the ball exactly horizontally. As you watch him throw, the pitches seem to vary from 50 below horizontal to 50 above horizontal. What is the range of speeds with which the ball might have left his hand? Enter the minimum and the maximum speed of the ball. Enter your answers using two significant figures separated by a comma.

Explanation / Answer

Part-B : As you watch him throw, the pitches seem to vary from 50 below horizontal to 50 above horizontal.

At 50 below horizontal, we have

vo,x = vo cos 50

vo,x = (0.996) vo                                                                     { eq.1 }

And vo,y = vo sin 50

vo,y = (0.087) vo                                                                       { eq.2 }

using an equation, x = vo,x t

then (20 m) = (0.996) vo t

vo t = 20.08 m                                                         { eq.3 }

using equation of motion 2,

y = voy t + (1/2) a t2

(7 m) = (0.087) vo t + (0.5) (9.8 m/s2) t2

(7 m) = (0.087) (20.08 m) + (4.9 m/s2) t2   

(7 m) = (1.74 m) + (4.9 m/s2) t2

(5.26 m) = (4.9 m/s2) t2

t2 = 1.073

or t = 1.035 sec

now, inserting the value of 't' in eq.3,

vo t = 20.08 m

vo = (20.08 m) / (1.035 s)

vo = 19.4 m/s

At 50 above horizontal, we have

using equation of motion 2,

y = voy t + (1/2) a t2

(7 m) = -(0.087) vo t + (0.5) (9.8 m/s2) t2

(7 m) = -(0.087) (20.08 m) + (4.9 m/s2) t2   

(7 m) = -(1.74 m) + (4.9 m/s2) t2

(8.74m) = (4.9 m/s2) t2

t2 = 1.783

or t = 1.33 sec

now, inserting the value of 't' in eq.3,

vo t = 20.08 m

vo = (20.08 m) / (1.33 s)

vo = 15.09 m/s

The range of speeds with which the ball might have left his hand will be given as ::

vmin = 15.09 m/s            and               vmax = 19.4 m/s

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