Part A Find v 0 , the initial speed. Use g = 9.80 m / s 2 for the magnitude of t

Question

Part A Find v0, the initial speed. Use g=9.80m/s2 for the magnitude of the acceleration due to gravity Part B Find the angle ? in degrees. Express your answer numerically in degrees to three significant figures. Part C Find a vector expression for the velocity v? of the softball 0.100 s before the ball is caught. Use the notation vx, vy, an ordered pair of values separated by a commas Express your answer numerically in meters per second to three significant figures. Part D Find a vector expression for the position r? of the softball 0.100 s before the ball is caught. Use the notation x, y, an ordered pair of values separated by a comma, where x and y are expressed numerically in meters, as measured from the point where the softball initially left the bat. Express your answer to three significant figures.


Part A Find v0, the initial speed. Use g=9.80m/s2 for the magnitude of the acceleration due to gravity Part B Find the angle ? in degrees. Express your answer numerically in degrees to three significant figures. Part C Find a vector expression for the velocity v? of the softball 0.100 s before the ball is caught. Use the notation vx, vy, an ordered pair of values separated by a commas Express your answer numerically in meters per second to three significant figures. Part D Find a vector expression for the position r? of the softball 0.100 s before the ball is caught. Use the notation x, y, an ordered pair of values separated by a comma, where x and y are expressed numerically in meters, as measured from the point where the softball initially left the bat. Express your answer to three significant figures.


Part B Find the angle ? in degrees. Express your answer numerically in degrees to three significant figures. Part C Find a vector expression for the velocity v? of the softball 0.100 s before the ball is caught. Use the notation vx, vy, an ordered pair of values separated by a commas Express your answer numerically in meters per second to three significant figures. Part D Find a vector expression for the position r? of the softball 0.100 s before the ball is caught. Use the notation x, y, an ordered pair of values separated by a comma, where x and y are expressed numerically in meters, as measured from the point where the softball initially left the bat. Express your answer to three significant figures. Find a vector expression for the velocity v? of the softball 0.100 s before the ball is caught. Use the notation vx, vy, an ordered pair of values separated by a commas Express your answer numerically in meters per second to three significant figures. Part D Find a vector expression for the position r? of the softball 0.100 s before the ball is caught. Use the notation x, y, an ordered pair of values separated by a comma, where x and y are expressed numerically in meters, as measured from the point where the softball initially left the bat. Express your answer to three significant figures. Part D Find a vector expression for the position r? of the softball 0.100 s before the ball is caught. Use the notation x, y, an ordered pair of values separated by a comma, where x and y are expressed numerically in meters, as measured from the point where the softball initially left the bat. Express your answer to three significant figures.

Explanation / Answer

Let the x axis be the line from home through third base
Let the height above bat be Z

First find how far the ball tralled in x direction.
X = Xo + V t
X = 18 + 7 * 2
X = 32 m from home plate

t = 2 secs

Vx = 32 / 2 m/s
16 m/s

Know consider component of velocity in vertical direction
Z = Zo + Vzo*t + 0.5 * Az * t^2
Z = 0 + Vzo*t + 0.5* -9.8 * t^2

But when the ball is caught Z = 0
Vzo*t + 0.5* -9.8 * t^2 = 0

t(Vzo - 4.9*t) = 0

this expression is only equal to zero when :
t = 0 The time of the batter hitting the ball
Vzo - 4.9t = 0
but we know the ball was in the air for two secs
Vz0 4.9*2
Vz0 = 9.8 m/s

In vector notation (do you know this? Its very cool. I is a vector one unit long in the x direction, k is a vector one unit long in the z direction, cf Rec notation and Polar notation))
Vo = 16 * I + 9.8 * k

|Vo| = sqrt(16^2 + 9.8^2)
|Vo| = 18.7 m/s

Part 2. Theta in degrees

Tan(@) = 9.8/16
0.6125
@ ATAN(9.8/16)
@ 0.549 rad
@ .555*180/pi()
@ 31.8 degrees

3
Can I use vector notation now I have explained it?

Vx = 16
Vz = 9.8 - 9.8*t

So V = 16* i_ + (9.8 - 9.8*t) * k_

So 0.1 secs before catch t = 1.9secs
So substitute into your velocity equation
Vx = 16
Vz = 9.8 - 9.8*1.9
Vz = -8.82 m/s Looks good - not quite -9.8 m/s = speed at catching)

Convert into polar notation

V = sqrt(16^2+(-8.82)^2)
V = 18.3 m/s

@ atan(-8.82/16)
-28.9 degrees Looks good not quite but almost the launch angle

4

X(t) = 16*t
Z(t) = Voz * t - 0.5*9.8*t^2

Rvec = 16*t*i_ + (Voz * t - 0.5*9.8*t^2)*k_

Substitute in t = 1.9secs

X = 30.4 m Almost but not quite 32m
Z = 0.931 m Almost but not quite zero

Polar notation

r = sqrt(30.4^2+0.931^2)
r = 30.4142526
@ Atan(0.931/30.4) Almost but not quite 32m
@ 1.75 degrees Almost but not quite zero

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