1. A baseball is seen to pass upward by a window 28 m above the street with a ve
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Question
1. A baseball is seen to pass upward by a window 28 m above the street with a vertical speed of 10 m/s. The ball was thrown from the street.
(a) What was its initial speed?
m/s
(b) What altitude does it reach?
m
(c) How long after it was thrown did it pass the window?
s
(d) After how many more seconds does it reach the street again?
s
2. You are given a vector in the xy plane that has a magnitude of 90.0 units and a y component of -60.0 units. What are the two possibilities for its x component?
(a) Give the resultant in terms of components.
Rx =
Ry =
(b) What is the magnitude of the resultant?
What is the resultant's angle above the +x axis?
°
Explanation / Answer
Ans.-1 (a) What was its initial speed?
Let, initial speed of the ball = u
As per equation of motion: v2= u2 + 2ah
Here u = initial velocity
a = -g = acceleration due to gravity (it is acting in the opposite direction of motion)
h = 28 m (Height of window)
v=10 m/s at window
putting the value in the equation: v2=u2+2* (-g)*h
u2 = v2 - 2gh
Here g= 9.8 m/s2
u2= 102 - (2*9.8*28)
u = sqrt (648.8)
u= 25.47 m/s
(b) What altitude does it reach?
As per equation of motion: v2= u2 + 2ah
v = 0 at the peak point
u = 25.47 m/s
a = -g = -9.8 m/s2
putting the values in the above equation: 0 = (25.47)2 – 2* (9.8)* h
h = (25.47)2/ (2*9.8)
h = 33.1 m
(c) How long after it was thrown did it pass the window?
As per equation of motion: v = u + at
here v= 10 m/s
u= 25.47 m/s
a =-g =-9.8 m/s2
putting the value in the equation: 10 = 25.47- 9.8* t
t = (25.47 – 10)/ 9.8
t = 1.58 s
(d) After how many more seconds does it reach the street again?
As per the equation of motion: S = ut + ½*at2
S= displacement = 0
Putting the values in the equation-
0 = 25.47t -0.5* 9.8t2
4.9t2-25.47t = 0
t=0 &
t =25.47/4.9
t= 5.2 s
Value of displacement is ZERO, 2 times in this motion.
Ans 2- Let, vector = v
Magnitude of vector |v|= sqrt (x2 + y2)
|y|= -60
|x|2 = |v|2- |y|2
|x|2 = 902 – (-60)2
|x|= sqrt (8100-3600)
|x| = 67.1
Ans 3 - (a) Give the resultant in terms of components.
Rx = algebraic sum of components of all the vectors on x-axis
Rx = Ax + Bx + Cx
Rx = 60 cos 28 + (-40 cos 50) + 0 (Bx is along –ve x-axis)
Rx = 52.98 – 25.71
Rx = 27.27
Ry = algebraic sum of components of all the vectors on y-axis
Ry = Ay + By + Cy
Ry = 60 sin 28 + (40 sin 50) + (- 46.8) (Cy is along –ve y-axis)
Ry = 28.17 + 30.64 – 46.8
Ry = 12.01
(b) What is the magnitude of the resultant?
R = sqrt (Rx2+ Ry2)
R = sqrt {(27.27)2 + (12.01)2}
R = sqrt (743.6529 + 144.2401)
R = sqrt (887.893)
R = 29.78
(c) What is the resultant's angle above the +x axis?
Angle x ° = tan-1 (Ry / Rx )
x ° = tan-1 (12.01/ 27.27)
x ° = tan-1 (0.443)
x ° = 23.89°
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