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M M%%#h/%MrY[$o%%0&k$** /%* /%@%%&* : Physics 513 Name ______________________________
Vaughan Motion in a Plane Problems
1. A ball is thrown horizontally from the roof of a building at a speed of 8 m/s. The ball hits the ground 3 seconds later.
a) How far does it fall in those three seconds?
b) How far horizontally did it move in those three seconds (i.e. what was the range)?
2. A steel ball is projected horizontally at 20 m/s from the top of a 49 meter tall tower. How horizontally from the base of the tower does the projectile hit the ground?
3. A person standing on a cliff throws a stone with a horizontal velocity of 15 m/s. The stone hits the ground horizontally 68 m from the base of the cliff. What is the height of the cliff?
4. A package is in an airplane that is travelling horizontally at 150 m/s at an altitude of 490 m. The package is released from the moving airplane.
a) How long does it take the package to hit the ground?
b) How far forward from the spot over which the package was dropped does the package land?
c) If the plane continues on its flight path, where is the plane when the package hits the ground?
5. A steel ball is rolling horizontally with a constant velocity when it rolls off a table that is 0.95 meters tall. It hits the ground 2.2 meters horizontally from the base of the table. What was that initial velocity?
6. A projectile is launched horizontally from the top of a building with a velocity of 8 m/s. The object hits the ground 15 meters from the base of the building.
a) What is the height of the building?
b) Right before the projectile hits the ground, what is its instantaneous horizontal velocity?
c) Right before the projectile hits the ground, what is its instantaneous vertical velocity?\
d) Right before the projectile hits the ground, what is its speed?
7. Another ball is thrown horizontally from the same building as in number 6 except this time the ball is launched at a speed of 16 m/s. find the range, time, instantaneous final vertical and horizontal velocities and then answer the following:
a) What happened to the time it took to fall compared to in 6?
b) What happened to the range compared to in 6?
c) What happened to the final horizontal velocity compared to in 6?
d) What happened to the final vertical velocity compared to in 6?
8) A book is thrown horizontally off the top of a building that is 20 meters tall. Right before the book hits the ground, it has a speed of 30 m/s
a) How much time does it take the book to hit the ground?
b) What is the vertical velocity just before the book hits the ground?
c) What is the horizontal velocity just before the book hits the ground?
d) What is the range of the book?
9) A football is thrown on a perfectly flat field such that it has an initial vertical velocity of 50 m/s and an initial horizontal velocity of 20 m/s. It is caught at the same height it is thrown
a) What is the total time of travel?
b) What is the range?
c) What is the maximum height? When does the ball achieve this?
10) A soccer ball is kicked on a level field. The initial velocity of the ball just after the kick is 60 m/s at an angle of 37o to the ground.
a) Find the total time of flight.
b) Find the range
c) Find the maximum height.
d) Find the speed of the ball at the maximum height.
e) Find the speed of the ball after 5 seconds.
11) A rock is tossed with an initial velocity of 30 m/s on flat ground. Find the range and time of travel if the angle of launch is
a) 30o b) 45o c) 60o
12) An arrow is shot with a certain velocity straight upwards from the ground. It achieves a maximum height of 60 meters. If this same arrow were shot at a 45 degree angle with the same initial speed at which it was fired upwards,
a) how far horizontally would it go?
b) what would be the maximum height for the parabolic path?
13) A football is kicked on level ground at an angle. The ball is caught 4.3 seconds later at the same height and 70 m horizontally from where it is thrown
a) What was the initial horizontal velocity?
b) What was the initial vertical velocity?
c) What was the magnitude of the initial speed?
d) What angle did the initial speed make with the ground?
e) What maximum height was reached?
14) A cannon is set up on the top of a cliff. The
cannon is pointed up at an angle of 20 degrees.
The cannonball leaves the cannon with a speed
of 100 m/s. The cliff is 300 meters high.
a) Find the total time of flight.
b) Find the range
c) Find the speed of the cannonball just before it lands.
d) Find the maximum height
15) A target is set up 50 meters from an archer. The bulls eye is exactly level with the archers arms. If the archer can fire the arrow with an initial speed of 80 m/s, what angle to the horizontal should the arrow be fired at to get a bulls eye?
16) A projectile cannonball is launched from the ground
at a 50 degree angle with a speed of 100 m/s as shown.
It hits the target which is 80 m above on the top of a
cliff ON ITS WAY DOWN.
a) State the total vertical displacement
b) Find the time it takes to hit the target.
c) How far away from the base of the cliff was the cannon?
d) What is the horizontal velocity of the cannonball when
it strikes the target?
e) What is the vertical velocity of the cannonball when it
strikes the target?
f) What is the speed of the cannonball when it hits?
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