This solution uses a coordinate system where the pumpkin starts at (xo, yo) = (0,0) and ends at (x, y) = (d, 0). Other solutions can pick a different origin with the same results. Plugging in: d = (vo cos 0o) tair (Eqn. 1) 0 = (vo sin 0o) tair - gtir (Eqn. 2) We now have 4 variables and 2 equations (assuming g = 9.8 is known). If 2 variables are given, the equations can be solved. Note that will be a given variable for projectile motion in Physics 121 to avoid overly complicated trigonometric equations. Question: VO El m S Type your answer... vo 127m Type your answer... 00 30.4° 00 34.3⁰ d 1,377m tair S 40
This solution uses a coordinate system where the pumpkin starts at (xo, yo) = (0,0) and ends at (x, y) = (d, 0). Other solutions can pick a different origin with the same results. Plugging in: d = (vo cos 0o) tair (Eqn. 1) 0 = (vo sin 0o) tair - gtir (Eqn. 2) We now have 4 variables and 2 equations (assuming g = 9.8 is known). If 2 variables are given, the equations can be solved. Note that will be a given variable for projectile motion in Physics 121 to avoid overly complicated trigonometric equations. Question: VO El m S Type your answer... vo 127m Type your answer... 00 30.4° 00 34.3⁰ d 1,377m tair S 40
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Transcribed Image Text:This solution uses a coordinate system where the pumpkin starts at
(xo, yo) = (0,0) and ends at (x, y) = (d, 0). Other solutions can
pick a different origin with the same results. Plugging in:
d = (vo cos 00) tair
(Eqn. 1)
0 = (vo sin 0o) tair -
We now have 4 variables and 2 equations (assuming g = 9.8 is
known). If 2 variables are given, the equations can be solved. Note
that will be a given variable for projectile motion in Physics 121 to
avoid overly complicated trigonometric equations.
Question:
vo
m
Type your answer...
VO
127™
gtir (Eqn. 2)
Type your answer...
00
30.4°
00
34.3⁰
d
1,377m
tair
S
11-
Transcribed Image Text:Physics
Background to question:
Projectile Motion (start and end at same height)
Punkin' Chunkin' is an event where competitors launch pumpkins as
far as they can into a corn field. For simplicity, assume the
pumpkins land at the same height they were launched from. Ignore
air resistance.
A pumpkin has a launch speed of vo and a launch angle of 00. The
pumpkin was in the air for a time of tair and lands a horizontal
distance of d away from the launch point.
Solution:
The projectile motion equations:
x = x + (vo cos 00) t
y = yo + (vo sin 0o) t - gt²
This solution uses a coordinate system where the pumpkin starts at
(xo, yo) = (0,0) and ends at (x, y) = (d, 0). Other solutions can
pick a different origin with the same results. Plugging in:
d = (vo cos 00) tair (Eqn. 1)
0 = (vo sin 0o) tair - gtir (Eqn. 2)
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