Mechanics | Relativity Answers

3. A projectile leaves the ground with initial velocity of 30 m/s, at an angle of θ above the

horizontal. At maximum height, the velocity of the projectile is half of its initial velocity.

a) Calculate the angle, θ of the projectile motion [2]

b) Calculate the time, ttotal needed for the projectile to reach the ground. [3]

A parol (Christmas lantern) made of bamboo sticks and covered in colored paper is hung on a string on a window. If the parol has a mass of 100 g, and is in equilibrium, what is the tension in the string?

A block of mass m1 is suspended vertically with a rope connected to a block of mass m2. The block of mass m2 is on a frictionless plane inclined at theta with respect to the horizontal. If m1=2kg, the acceleration of the block is 1.96 m/s^2 downward. If m1=1kg the acceleration of the block is 1.22 m/s^2 upwards. Determine theta (angle) and m2.

Two blocks of masses m1=3kg and m2=5kg connected by a rope of negligible mass and slide on a frictionless surface. A force of 10 N acts on m2 at a 20 degree angle to the horizontal. Find a) the acceleration of m1 as well as it's orientation b) the tension in the rope.

The diagram is similar to that in this linked image: http://gauss.vaniercollege.qc.ca/pwiki/images/a/aa/N_APP_EX_4.png

2. The figure below shows the acceleration of a 10 kg package that is accelerated to a maximum acceleration of a. = 20 m/s2 . How much work did the force used to accelerate the package do in order to move it from 0 m to 8 m?

5. Kilauea in Hawaii is the world’s most continuously active volcano. Very active volcanoes characteristically eject red-hot rocks and lava rather than smoke and ash. Suppose a large rock is ejected from the volcano with a speed of 25.0 m/s and at an angle 35.0º above the horizontal. The rock strikes the side of the volcano at an altitude 20.0 m lower than its starting point.

a. Calculate the time it takes the rock to follow this path.

b. What are the magnitude and direction of the rock’s velocity at impact?

1. If an arrow is fired from a bow with a perfectly horizontal velocity of 60.0 m/s and the arrow was 2.00 m above the ground when the it was released, how far will the arrow fly horizontally before it strikes theground?

2. A rock was thrown horizontally from a 100.0 m high cliff. It strikes the ground 90.0 m from the base of the cliff. At what speed was it thrown?

3. A cliff diver running 3.60 m/s dives out horizontally from the edge of a vertical cliff and reaches the water below 2.00 s later. How high is the cliff and how far from the base of the cliff did the diver hit the water?

4. During a fireworks display, a shell is shot into the air with an initial speed of 70.0 m/s at an angle of75.0º above the horizontal. The fuse is timed to ignite the shell just as it reaches its highest point above the ground.

a. Calculate the height at which the shell explodes.

b. How much time passed between the launch of the shell and the explosion?

c. What is the horizontal displacement of the shell when it explodes?

A liker walk 53.1 degree north of east for 2.5km then due east for 2km. What is her total displacement from her starting point if you measure the distance along straight line?

Displacement in linear motion is a vector quantity but angular displacement is not.Explain

vector A points north and vector B points east. If vector C=B-A, then vector C points