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.

 

[m2003]

I tried using the equation d=vit+1/2at^2 and setting the initial velocity to 0 and using the time intervals given, but that didn't work either.

I would approach these problems by first understanding the basic principles of projectile motion. Projectile motion is a type of motion in which an object is thrown or projected into the air, and its path is determined by the forces acting on it, namely gravity and air resistance.

To solve the first problem, we can use the basic kinematics equation for horizontal distance, which is d = v*t, where d is the horizontal distance, v is the initial velocity, and t is the time. Since the rocks are ejected at a speed of 100 m/s, the initial velocity in the horizontal direction will also be 100 m/s. We can use this velocity and the time it takes for the rocks to reach sea level (1250 m high volcano) to calculate the maximum horizontal distance.

For the second problem, we can use the same equation, d = v*t, but this time we need to find the initial velocity in both the horizontal and vertical directions. To find the initial velocity in the vertical direction, we can use the equation vf = vi + at, where vf is the final velocity (which is 0 since the ball reaches the same height), vi is the initial velocity, a is the acceleration due to gravity (which is -9.8 m/s^2), and t is the time it takes for the ball to reach its maximum height. We can also use the same equation to find the initial velocity in the horizontal direction, but this time we need to use the horizontal distance and time it takes for the ball to reach the hoop. Once we have both initial velocities, we can use the Pythagorean theorem to find the total initial velocity.

For the third problem, we can use the same equations as the first two problems, but we need to take into account the fact that the ball is thrown in an evacuated tube. This means that there is no air resistance, so we can ignore it in our calculations. We can use the given time intervals and distance to calculate the initial velocity in both the horizontal and vertical directions, and then use the Pythagorean theorem to find the total initial velocity. Finally, we can use the equation vf = vi + at to solve for the acceleration due to gravity. If the calculated value is close to 9.8 m