Hw1.3 Free Fall
Friday, October 2, 2020
8:58 AM
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practice solving your problems by showing the process on a page in an organized and logical way as
modeled in class.
Free Fall Problems
Show you work with step-by-step solutions.
For each of the following problems, a complete solution consists of:
a) a well-labeled diagram of the situation
b) a list of all motion variables with givens, labeled with units and appropriate algebraic signs (+, -)
c) a clear presentation by showing the equation used before producing a numerical answer
Remember that if the boundary conditions change in a problem, you need to list new givens for it.
1. A body falls freely from rest on Earth. Find:
a. its displacement from t = 0 to t = 3s.
b. if it falls 2 xs longer (for 6 s), how much farther will it fall? (determine kinematic eqn that gives
relationship between t and y with other variables all not changing; you used it in part a)
c. the time for it to reach a speed of 25 m/s
d. the time to reach double the speed (50 m/s) (determine kinematic eqn that gives relationship between
t and v with other variables all not changing)
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e. the time required for it to fall 300 m
f. its speed after falling 70 m
g. if it falls 2 xs farther, by how much will the speed change (determine kinematic eqn that gives
relationship between y and v with other variables all not changing)
2. A marble dropped from a bridge strikes the water in 6.0 s. Calculate:
a. the speed with which it strikes the water
b. the height of the bridge
c. If the bridge were two times higher, by how much would the speed of the marble change when it hit the water?
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c. If the bridge were two times higher, by how much would the speed of the marble change when it hit the water?
d. If the bridge were two times higher, how much longer would it take for the marble to strike the water?
Free Fall with non-zero vo
3. A ball is thrown downward with an initial speed of 20 m/s on Earth. What is the:
a. acceleration of the object
b. displacement during the first 4 s
c. time required to reach a speed of 50 m/s
d. time required to fall 300 m (Hint: use g=-10m/s2 and factor the quadratic or use the quadratic formula)
e. speed after falling 100 m
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e. speed after falling 100 m
4. A rock is thrown upward with an initial speed of 15 m/s on Earth. What is the:
a. rock's height after 1 sec
b. time required to reach an upward speed of 3 m/s
c. time required to reach a downward speed of 5 m/s
d. maximum height of the rock?
A = -10 m/s^2
V0 = 15m/s
e. what is the acceleration of the rock at its maximum height?
f. If the rock were thrown upward on the moon with the same initial speed, how much would the max height
change? (on the moon, the acceleration due to gravity is 1/6th the value on Earth) (Hint:
(determine kinematic eqn that gives the relationship between a and y with other variables all not changing)
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change? (on the moon, the acceleration due to gravity is 1/6th the value on Earth) (Hint:
(determine kinematic eqn that gives the relationship between a and y with other variables all not changing)
5. A rock is thrown straight up with an initial speed of 22 m/s.
a. How long will it be in the air before it returns to the thrower (hang time)?
b. What is the maximum height of the rock?
c. If the rock were thrown upward on the moon with the same initial speed, how much would the hang time
change? (on the moon, the acceleration due to gravity is 1/6th the value on Earth)
6.
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6. A vertical punt has a hang time of 3.8 seconds.
What was its initial velocity?
Sketch the x-t graph and plot the v-t and a-t graphs of the object’s motion. Label the time axes on all graphs.
Next to each graph, write the equation that goes with the graph [x(t) = …. , v(t) = …, and a(t) = …]; the only
variables in the x(t) equation should be x and t, and the only variables in the v(t) equation should be v and t.
7. A student throws a rock off a 120 m high bridge with an initial downward speed of 10.0 m/s
a. How long does it take the rock to hit the ground below? (Hint: can use g=-10m/s2 and factor the quadratic or use
the quadratic formula)
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b. How fast is the rock going at the moment of impact?
c. Sketch the x-t graph and plot the v-t and a-t graphs of the rock’s motion. Label the time axes on all graphs. Next to
each graph, write the equation that goes with the graph [x(t) = …. , v(t) = …, and a(t) = …]; the only variables in
the x(t) equation should be x and t, and the only variables in the v(t) equation should be v and t.
8. When a kid drops a rock off the edge of a cliff, it takes 4.0 s to reach the ground below. When she throws the rock
down, it strikes the ground in 3.0 s. What initial speed did she give the rock? (Hint: there are two problems based on the
two sentences. List separate gives for each situation. Use the first to find a quantity that can be used in the second.)
9. To determine freefall acceleration on a moon with no atmosphere, you drop your handkerchief off the roof of a
baseball stadium there. The roof is 113 meters tall. The handkerchief reaches the ground in 18.2 seconds. What is freefall
acceleration on this moon? (State the result as a positive quantity.)
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10. A diver springs upward with an initial speed of 1.80 m/s from a board 3.00 m above the water
a) Find the velocity with which he strikes the water.
b) What is the highest point he reaches above the water?
11. Two rocks are thrown off the edge of a cliff that is 15.0 m above the ground. The first rock is thrown upward, at a
velocity of +12.0 m/s. The second is thrown downward, at a velocity of −12.0 m/s. Ignore air resistance. Determine
a) how long it takes the first rock to hit the ground
b) at what velocity it hits (that’s right before it hits).
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c) how long it takes the second rock to hit the ground
d) at what velocity the second rock hits.
12. To determine how high a cliff is, a llama farmer drops a rock, and then 0.800 s later, throws another rock straight
down at a velocity of −10.0 m/s. Both rocks land at the same time. How high is the cliff?
(Hint: There are 2 situations and so you need to list givens for each. Make sure that you use subscripts to indicate
different variables for rock1 and rock2 and determine if/how the variables for rock1 are related to rock2. Use the 2
equations that can be generated from both rocks to solve for 2 unknowns)
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Answers
1a) -44.1m b) 4xs farther c) 2.55 s d) 2xs longer (5.1s) e) 7.82s f) 37 m/s
2a) 58.8 m/s b) 176.4 m c) 2 xs d) 2 xs longer
3a) -9.8 m/s2 b) -158.4m c) 3.1s d) 6 s e) 48.6 m/s
4a) +10.1 m b) 1.22s c) 2.04s d) 11.5 m e) 9.8m/s2 down e) increase 6xs
5a) 4.49 s b) 24.7m c) increase 6xs
6. 18.6 m/s
7a) 4 s b) 49.5 m/s
8. -11.4 m/s
9. 0.682 m/s2
10a) 7.88m/s downward b) 3.165m above the water
11a) 3.36s b) -20.9m/s c) 0.91s d) -20.9 m/s
12. 24.8 m
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g. 2 xs