- #1
lNVlNClBLE
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Hopefully I learned a few things from the previous thread and got some of this right.
Refer to the diagram. The ball is thrown with the parameters given on the diagram. a) Compute the total height the ball reaches and the height the ball will reach above the building. b) Compute the x-displacement the ball reaches from the base of the building. c) With what velocity does the ball hit the ground?
Height of building = 45.0m
Initial velocity = 20.0 m/s
Angle thrown = 30.0 degrees
Ymax = Vot + (1/2)at^2
V = sqrt Vx^2 + Vy^2
Quadratic
Delta(y) = Voy(time) - (1/2)gt^2
a) v = Vo + at
0 = 20 + (-9.8)t
-20 = -9.8t
t = 2.04s
Ymax = Vot + 1/2 at^2
20(2.04) + 1/2 (9.8)(4.16)
40.8+20.38 = 61.18m
61.18 - 45 = 16.18m
b) Vox = Vo Cos(Theta) = (20m/s)(cos30) = 17.3 m/s
Voy = Vo Sin(Theta) = (20m/s)(sin30) = 10 m/s
Delta(y) = Voy t - 1/2gt^2
-45 = (10m/s)t + (-4.9)t^2
-4.9t^2 + 10t + 45 = 0
4.9t^2 - 10t - 45 = 0
x = 10 + sqrt 100-4(4.9(-45)/9.8
x = 10 + sqrt 100+882/9.8
x = 10 + 31.34/9.8
x = 4.22 seconds
Vo Cos(Theta)t = (20m/s)(cos30)(4.22)
= (20)(.866)(4.22)
= 73.09m
c)
Vy = Vo Sin(Theta) - gt
= (20 m/s)(1/2) - (9.8)(4.22)
= 10 m/s - 41.36 = -31.4 m/s
V = sqrt Vx^2 + Vy^2
= sqrt (17.3)^2 + (-31.4)^2
= sqrt 299.30 + 985.96
= sqrt 1285.26
= 35.85 m/s
Homework Statement
Refer to the diagram. The ball is thrown with the parameters given on the diagram. a) Compute the total height the ball reaches and the height the ball will reach above the building. b) Compute the x-displacement the ball reaches from the base of the building. c) With what velocity does the ball hit the ground?
Height of building = 45.0m
Initial velocity = 20.0 m/s
Angle thrown = 30.0 degrees
Homework Equations
Ymax = Vot + (1/2)at^2
V = sqrt Vx^2 + Vy^2
Quadratic
Delta(y) = Voy(time) - (1/2)gt^2
The Attempt at a Solution
a) v = Vo + at
0 = 20 + (-9.8)t
-20 = -9.8t
t = 2.04s
Ymax = Vot + 1/2 at^2
20(2.04) + 1/2 (9.8)(4.16)
40.8+20.38 = 61.18m
61.18 - 45 = 16.18m
b) Vox = Vo Cos(Theta) = (20m/s)(cos30) = 17.3 m/s
Voy = Vo Sin(Theta) = (20m/s)(sin30) = 10 m/s
Delta(y) = Voy t - 1/2gt^2
-45 = (10m/s)t + (-4.9)t^2
-4.9t^2 + 10t + 45 = 0
4.9t^2 - 10t - 45 = 0
x = 10 + sqrt 100-4(4.9(-45)/9.8
x = 10 + sqrt 100+882/9.8
x = 10 + 31.34/9.8
x = 4.22 seconds
Vo Cos(Theta)t = (20m/s)(cos30)(4.22)
= (20)(.866)(4.22)
= 73.09m
c)
Vy = Vo Sin(Theta) - gt
= (20 m/s)(1/2) - (9.8)(4.22)
= 10 m/s - 41.36 = -31.4 m/s
V = sqrt Vx^2 + Vy^2
= sqrt (17.3)^2 + (-31.4)^2
= sqrt 299.30 + 985.96
= sqrt 1285.26
= 35.85 m/s