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A toy car rolls off a table and falls to the floor 1.25 m below. It hits the floor 2.30 m
away from the table.
A. How long does the car take to hit the floor?
B. What speed is the car traveling as it leaves the table?
C. How fast is the car moving VERTICALLY when it hits the ground?
ANSWERS
Known:
Δx = 2.30 m
Δy = -1.25 m
Vyi = 0 m/s (car is moving horizontally only)
A) Solving for Δt:
Formula:
Δy = v y i Δt + 12 gΔt 2
Work:
−1.25m = .5(−9.81 sm2 )Δt 2
Answer:
Δt = 0.505s
B) Solving for vx:
Formula:
Δx = v x Δt
Work:
2.30 = v x (.505s)
Answer:
v x = 4.56 ms
c) Solving for vyf:
Formula:
2
2
v y f = v y i + gΔt or: v y f = v y i + 2gΔy
Work:
v y f = −9.81 sm2 (.505s) or: v y f = 2(−9.81 sm2 )(−1.25m)
Answer: €
v y f = −4.95 ms
€
An arrow is launched with a horizontal velocity of 35.5 m/s and a vertical velocity of 50.0
m/s.
A. What is the angle it is shot at?
B. What is its initial speed?
C. How high does it get?
D. How high is the arrow when its vertical velocity is –10.0 m/s?
E. How long is it in the air?
F. How far away does it land? (solve e first)
ANSWERS
Known:
v x = 35.5 m/s
v yi = 50.0 m/s
B)Solving for vi:
A) Solving for θ:
v yi
Formula: Pythagorean Theorem
tan θ = v x
Formula:
Work:
Work:
2
θ = tan−1 50.0
35.5
Answer:
€
v i = 35.5 ms + 50.0 ms
2
Answer:
v i = 61.3 ms
θ = 54.6°
€
C) Solving for Δy:
2
2
v y f = v y i + 2gΔy
Formula:
€
Work:
2
2
0 ms − 50 ms
Δy =
€2(−9.81 sm2 )
Work:
(−10.0 ms ) 2 − (50.0 ms ) 2
Δy =
2(−9.81 sm2 )
€
Answer:
Δy = 122m
Answer:
Δy = 127m
E) Solving for Δt:
v y f = v y i + gΔt
Formula:
€
€
Work:
−50.0 ms − 50.0 ms
Δt =
m
€ −9.81 s2
F) Solving for Δx:
Formula:
Δx = v x Δt
Work:
Δx = (35.5 ms )10.2s
€
Answer:
Answer:
Δt = 10.2s
D) Solving for Δy:
2
2
v y f = v y i + 2gΔy
Formula:
€
€
Δx = 362m
A cannonball is shot out of a cannon at 45.0 m/s with an angle of 20° from horizontal.
A. What is the cannonball’s vx?
B. What is the cannonball’s vyi?
C. How high is the cannonball when its vy is 5.00 m/s?
D. How high does the cannonball get?
E. How long does it take the cannonball to reach its maximum height?
F. How long is the cannonball in the air?
ANSWERS
Known:
v i = 45.0 m/s
θ = 20.0°
A) Solving for vx:
Formula:
v x = v i cosθ
Work:
v x = 45 ms (cos20°)
Answer:
€
B) Solving for vyi:
Formula:
v x = v i sin θ
Work:
v x = 45 ms (sin20°)
Answer:
€
v x = 42.3 ms
€
C) Solving
for Δy:
€
2
2
v y f = v y i + 2gΔy
Formula:
€
D) Solving
for Δy:
€
2
2
v y f = v y i + 2gΔy
Formula:
2
Work:
€
Answer:
Δy =
(5.00 ms ) − (15.4 ms )
(
2 −9.81 sm2
Δy = 10.8m
€
E) Solving
for Δt:
€
v y f = v y i + gΔt
Formula:
0.00 ms −15.4 ms
−9.81 sm2
Work:
Δt =
Answer:
€
Δt = 1.57s
€
€
v x = 15.4 ms
)
2
2
(0.00 ms ) − (15.4 ms )
Work:
Δy =
€
Answer:
Δy = 12.1m
(
2 −9.81 sm2
)
€
F) Solving
for Δt:
€
v y f = v y i + gΔt
Formula:
−15.4 ms −15.4 ms
−9.81 sm2
Work:
Δt =
Answer:
€
Δt = 3.14s
€
€
2