2.Q1) (15 points) In the diagram below, M1 = 50 Kg, M2 = 20 Kg, mass and radius of the
g and 30 cm each, respectively. Both M1 and M2 rest on frictionless surfaces and the system starts from rest.
(a) Draw the fbd for each of M1, M2 and the pulley.
(b) Write the equations of motion for each of M1, M2 and the pulley.
(c) Calculate the linear acceleration of the two masses, as well as the angular acceleration of the pulley.
(d) Calculate the angular velocity of the pulley after M1 and M2 have been displaced linearly by 2 m.
Q2) (10 points) A basketball is thrown with an initial speed v0 of 10.8 m/s at 400 above horizontal, and it enters the hoop from above. The ball is released at 2.00 m above the ground. The hoop is 3.05 m above the ground and 10.0 m away from the player.
(a) Find the time at which the ball passes through the hoop.
(b) Find the ball’s velocity (express in component form) just when it enters the hoop.
(c) Find the ball’s maximum height.
Q3) (5 Points) An object is thrown up from the top of a building of height of 400 m with an initial velocity of 20 m/s.
(a) Find the position and the velocity of the object 5 s later.
(b) With what velocity will it hit the ground?
(c) At the same time the first object is thrown up, a second object is thrown up from the ground at 100 m/s. Will the two objects collide? If yes, calculate when and where,
3.A force of 40.0 N is needed to compress a spring 0.200 m. A 1.00 x 10-2 kg ball
a) Calculate the work done to compress the spring. (2 marks)
b) What happens to the work done on the spring ? (1 mark)
c) If the spring is released, what happens to the energy of the spring? (1 mark)
d) Calculate the total mechanical energy of the ball at the instant it leaves the spring. (2 marks)
e) What will be the speed of the ball at the instant it leaves the spring? (2 marks)
f) If the ball is fired up into the air by the spring, how much gravitational potential energy will it gain? (1 mark)
g) What will be the maximum height of the ball? (2 marks
5.Honestly I don't even know where to begin... I'm 15 years old and I've been homeschooled all my life. A
. A few years back I kinda dropped the ball with school. If I didn't understand something, I gave up on it. Because of that I've been pretty behind for quite a while now, but this year I decided to change and become a better student. There's still a few things I'm not entirely great at, but out of them all math is one that I suffer from the most. Geometry hasn't been too hard up until now, but I never quite understood certain aspects of Algebra and my current Geometry lessons require some algebraic knowledge which is what I lack. I've tried doing it on my own but I don't understand things easily, Khan Academy is super helpful but most of the time, the amount of knowledge overwhelms me and I don't learn a thing from the video/lesson. I know this is not going to be a simple one and done fix, but I know that I can't just keep passing by without improving my math skills so that's why I came here. I don't know how this works or if it's even going to help, but right now I think it's worth the try. Thank you in advance.
6.1.A group of penguins has 10 emperor penguins and 7 adelie penguins. How many ways are there to form a
a penguin aquarium with 6 penguins such that there are only at most 3 emperor penguins?
2. A gold pen,2 red pens, and 9 black pens are to be distributed among Alicia,Alice,Alma, and Aurora. A "Wonderful Set" is a set of pens that contains a gold ball pen but not a red pen. How many distinct ways can the pens be distributed among the girls such that one of the girls receives a Wonderful set and that she receives strictly the fewest pens?Assume pens of the same color are indistinguishable.
3.AMS is producing a set of commemorative license plates. Each license plate contains 5 characters from the string "AMS2020". How many license plates can be made?
4 Eight students including Take,Taki,Taka are to be arranged to sit at a circular table.How many ways can this be done if Taki and Take must sit diametrically opposite to each other,and that Taka must not sit beside Taki?
7.1. A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground.
ance is negligible, what is the ball’s speed at the instant it reaches its maximum height from the ground?
A. - 20 m/s
B. 0 m/s
C. + 17.3 m/s
D. + 10 m/s
E. + 20 m/s
2. A rhino charges full speed at a car with an initial velocity of 15 m/s. When the rhino collides with the car, it crumples in by 1 m before the rhino comes to a complete stop. What acceleration did the rhino feel as it came to a stop?
A. - 112.5 m/s^2
B. - 7.5 m/s^2
C. - 30 m/s^2
D. + 112.5 m/s^2
E. + 30 m/s^2
F. + 7.5 m/s^2
3. Two students want to determine the speed at which a ball is released when thrown vertically upward into the air. One student throws the ball into the air while the other student measures the total time that the ball is in the air. The students use a meterstick to measure the release height of the ball. Which of the following equations should the students use to determine the speed at which the ball was released? *
A. Use y final = y initial+ v initial *t + (1/2)*a*t^2 from the moment in time in which the ball was released to the moment in time in which the ball reaches its highest point.
B. v final^2 = v initial ^2 + 2a(????y) from the moment in time in which the ball was released to the moment in time in which the ball hits the ground.
C. Use y final = y initial+ v initial *t + (1/2)*a*t^2 from the moment in time in which the ball was released to the moment in time in which the ball hits the ground.
D. v final^2 = v initial ^2 + 2a(????y) from the moment in time in which the ball was released to the moment in time in which the ball reaches its highest point.