Cars and Rockets
Symbolic
Freely Flying Objects
Sports
Graphing Data to a linear fit
100
A 0.32kg toy car started from rest and accelerated forwards over a distance of 2.4m at which point it reached a maximum speed of 3.6m/s. What was the acceleration of the toy car.
2.7m/s2
100
A purse of mass M is dropped from the roof of a building of height H. What is the speed of the purse right before it hits the ground? Express all answer in terms of fundamental constants and given quantities.
√ (2gH)
100
A 24.6kg television is dropped from the top of a 34m tall building. How long does it take for the television to hit the ground?
2.63 seconds
100
A batter hits a pop fly straight into the air and it spends a total time of 3.4 seconds in the air before being caught. With what velocity did that ball leave the bat?
16.7 m/s
100
How could you plot the following relationship to get a linear graph? M2=2D + 3 (i.e. what could be the y axis, x axis) And what would the slope and y intercept represent?
y=M2
x=D
m=2
b=3
or other possible answers
200
A 3,260kg Lamborghini is driving at 44.3m/s when it slams on the brakes and skids to a stop. If the Lamborghini experienced constant deceleration of magnitude 34m/s2 while it was skidding, how many meters long were the skid marks it created on the road?
28.9 meters
200
A rock of mass M is thrown upwards from the ground with a speed U. How high does the rock make it above the ground?
U2/(2g)
200
A 12kg chair is dropped from the top of a 23m tall building. What is the velocity of the chair right before it hits the ground?
-21.2 m/s (must have the negative sign)
200
A football is punted poorly and it goes straight upwards. If the ball left the foot of the punter with a speed of 34.5m/s how high in the air does the ball make it?
60.7m
200
How could you plot the following relationship to get a linear graph? 2√H=4D2 - 9 (i.e. what could be the y axis, x axis) And what would the slope and y intercept represent?
y=2√H
x=D2
m=4
b=-9
or other possible answers
300
A rocket starts from the ground and is launched upwards by a thruster that acts on it for 4.3seconds. The constant acceleration provided by the thruster has a magnitude of 51.3m/s2. What is the altitude of the rocket when the thruster stops?
474 meters
300
A motorcycle of mass M starts from rest at a stoplight and speeds up with a constant acceleration A until it reaches a speed U. After reaching speed U it continues to travel with constant speed for a distance D. How much time in total did it take for the process described above?
U/A + D/U
300
A 1.5kg potato is thrown upwards with a speed of 34m/s from the street next to a 40m tall building. How high does the potato make it above the roof of the building?
18.97m above the roof (or rounding 19.0m above the roof)
300
When the running back grabs the football he is moving with a speed of 6.2m/s, but he immediately runs into the defensive line which slows him with constant deceleration until stopping him 2.3 meters in front of where he took the ball. How many seconds did it take the running back to be stopped by the defensive line?
0.74 seconds
300
How could you plot the following relationship to get a linear graph? D√H=5 (i.e. what could be the y axis, x axis) And what would the slope and y intercept represent?
y=√H
x=1/D
m=5
b=0
or other possible answers
400
A person of mass M falls out of the window of a burning building. He free falls for a time T until he hits a net which causes him to slow down with a constant deceleration of magnitude A. How long after hitting the net, did it take the net to slow the person to a stop. Give your answer in terms of fundamental constants and given variables.
(gT)/A
400
A truck of mass M drives with a constant speed U for a time t1. Then the driver slows with constant deceleration of magnitude As until coming to a stop. How far did the truck travel for the total time described above?
Ut1 + U2/(2As)
400
You stand on the roof of a 52m tall building. You drop a glass vase from the roof, and then 1.2 seconds later you drop another vase of twice the mass. At the moment the first vase crashes into the ground, how far below the roof is the second (heavier) vase?
20.7m below the roof of the building (the mass does not matter)
400
Kobe Bryant is on the roof of the Staples Center and he kicks a basketball straight upwards with a speed of 27.1 m/s. If the Staples Center is 45.7m tall, how long will it take the basketball to strike the ground at the bottom of the Staples Center?
6.89 seconds
400
You drop a ball repeatedly from different heights H and you measure the speed U of the ball right before it hits the ground. How could you plot your data so that it yields a linear graph, and what would the slope and y intercept represent?
y=U2 x=H
m=2g
b=0
or other possible answers
500
A rocket starts from the ground and is launched upwards by a thruster that provides a constant acceleration of magnitude of 78.2m/s2 until it reaches an altitude of 785m above the ground. How many seconds does it take the rocket to reach maximum velocity...and how many more seconds after that does it take to reach maximum altitude?
4.48 seconds to reach max velocity of 350m/s and 35.8 seconds after that to reach maximum altitude
500
A vampire of mass M starts from rest and speeds up with constant acceleration over a distance D reaching a speed U. Once it reaches a speed U the vampire travels with constant speed for a time T. Then the vampire slows to a stop with constant deceleration of magnitude A. How far in total did the vampire travel?
D + UT + U2/(2A)
500
A weather balloon holding 4.5kg of electronic monitoring equipment starts from the ground and travels upwards with a constant velocity of 8m/s until it reaches an altitude of 400m. However, at 400m the balloon pops. The monitoring equipment continues upwards for a while since it had an initial velocity but then it falls freely to the ground. How many seconds does the entire trip take?
59.9 seconds (do not accept 59.0 seconds since this does not include the initial velocity)
500
A hockey player of mass M starts from rest and speeds up with a constant acceleration A for a time T1 until reaching a maximum velocity. She travels with this maximum velocity for a time T2. Then the hockey player slows with constant deceleration to a stop in a time T3. How many meters in total did the hockey player travel?
½AT12 + AT1T2 + T3AT1/2
500
A spring launcher has a specific constant length over which it gives an initially stationary ball a constant acceleration. Different types of springs are used which provide different values of constant acceleration. The accelerations A are measured as well as the time T in the tube. How could you plot your data to get a linear graph which would allow you to determine the length of the tube, and what would the slope and y intercept correspond to?
y=T2
x=1/A
m=2D
b=0
or other possible answers
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