Projectile Motion Homework Solutions Using Basic Kinematics Equations

[Lorelyn]

Homework Statement

Volcanoes eject rocks at speeds of 100 m/s. Consider a 1250 m high volcano which ejects rocks in all directions. What is the maximum horizontal distance at sea level reached by the rocks?

Homework Equations

basic kinematics ones

The Attempt at a Solution

Well; I found the max height using initial and final velocity, and setting a as -g. That didn't help a whole lot though... So then I tried finding the initial velocity in the x-direction using trig (and assumed the angle was 45deg, because that is the best angle?). I got 70.716m/s. Which still didn't help me!
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Homework Statement

A basketball player throws the ball at a 35.0 deg angle above the horizontal to a hoop which is located a horizontal distance L = 4.80 m from the point of release and at a height h = 0.80 m above it. What is the required speed if the basketball is to reach the hoop?

Homework Equations

basic kinematics ones

The Attempt at a Solution

I actually don't know where to start with this one. I tried finding the veolcity for it to have a max. height > 0.8 and then used a triangle and trig to get the initial velocity but that failed...

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Homework Statement

At the National Physics Laboratory in England a measurement of the gravitational acceleration g was made by throwing a glass ball straight up in an evacuated tube and letting it return, as shown http://i14.photobucket.com/albums/a348/Drakhys-2/prob27a.gif The time interval between the two passages across the lower level is equal to DTL = 2.47 s. The time interval between the two passages across the upper level is equal to DTH = 1.20 s. The distance between the two levels is equal to H = 5.42 m. Calculate the magnitude of g.

Homework Equations

basic kinematics ones

The Attempt at a Solution

Well I know that in theory g should equal 9.8m/s^2. However to get that number I am very lost.

 

[Astronuc]

Try this site for a discussion on trajectories

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra4

If one has R($\theta$), then one can find max R, by differentiating with respect to $\theta$ and setting that to 0.