Assignment 16

course Phy 121

ú‰”Áãþ‘”’“ðqyf›Å’ÈžP±¢±ÍÍꃇwðassignment #016

016. Projectiles

Physics II

02-25-2008

......!!!!!!!!...................................

23:18:26

`q001. Note that this assignment contains 4 questions.

. How long does it take for an object dropped from rest to fall 2 meters under the influence of gravity?

......!!!!!!!!...................................

RESPONSE -->

Gravity is 9.8m/s^2. If the object falls 2 meters from rest you would divide 9.8m/s^2 by 2m:

This equals 4.9s^2

confidence assessment: 1

.................................................

......!!!!!!!!...................................

23:19:19

The object has initial velocity 0, acceleration 9.8 meters/second^2, and displacement 2 meters. We can easily solve this problem using the equations of motion.

Using the equation `ds = v0 `dt + .5 a `dt^2 we note first that since initial velocity is zero the term v0 `dt will be zero and can be dropped from the equation, leaving `ds = .5 a `dt^2. This equation is then easily solved for `dt, obtaining

`dt = `sqrt(2 *`ds / a ) = `sqrt(2 * 2 meters / (9.8 m/s^2) ) = .64 second.

......!!!!!!!!...................................

RESPONSE -->

I completely forgot this. I will study.

The object has initial velocity 0, acceleration 9.8 meters/second^2, and displacement 2 meters. We can easily solve this problem using the equations of motion.

Using the equation `ds = v0 `dt + .5 a `dt^2 we note first that since initial velocity is zero the term v0 `dt will be zero and can be dropped from the equation, leaving `ds = .5 a `dt^2. This equation is then easily solved for `dt, obtaining

`dt = `sqrt(2 *`ds / a ) = `sqrt(2 * 2 meters / (9.8 m/s^2) ) = .64 second.

self critique assessment: 3

.................................................

......!!!!!!!!...................................

23:23:02

`q002. While an object dropped from rest falls 2 meters under the influence of gravity, another object moves along a level surface at 12 meters/second. How far does the second object move during the time required for the first object to fall?

......!!!!!!!!...................................

RESPONSE -->

`dt = `sqrt(2 *`ds / a ) = `sqrt(2 * 2 meters / (9.8 m/s^2) ) = .64 second.

Since the first object moves in .64s then we multiply the other objects velocity by this amount of time:

12m/s * .64s = 7.68 meters

confidence assessment: 3

.................................................

......!!!!!!!!...................................

23:32:38

`q003. An object rolls off the edge of a tabletop and falls to the floor. At the instant it leaves the edge of the table is moving at 6 meters/second, and the distance from the tabletop to the floor is 1.5 meters.

Since if we neglect air resistance there is zero net force in the horizontal direction, the horizontal velocity of the object will remain unchanged.

Since the gravitational force acts in the vertical direction, motion in the vertical direction will undergo the acceleration of gravity. Since at the instant the object leaves the tabletop its motion is entirely in the horizontal direction, the vertical motion will also be characterized by an initial velocity of zero.

How far will the object therefore travel in the horizontal direction before it strikes the floor?

......!!!!!!!!...................................

RESPONSE -->

Since it takes the object 4 seconds to reach the ground (6m/s / 1.5m) we can multiply it's velocity by the time in the air to get it's distance.

6m/s * 4s = 24 meters of horizontal distance

6 m/s is not a vertical velocity, whereas 1.5 m is a vertical displacement. The two quantities can't be used in the same calculation.

If you did for some reason divide 6 m/s by 1.5 m your units would be 1/s, not s. (m/s) / m = (m/s) * (1/m) = 1/s.

If 6 m/s was your average vertical velocity (which is not the case) then you could divide the vertical displacement by the vertical velocity to get `dt = `ds / vAve, and you would get 1.5 m / (6 m/s) = .25 s.

However as I said above, 6 m/s is a horizontal velocity and has nothing to do with the vertical motion.

For the vertical motion you know that v0 = 0 (since the object was initially moving only in the horizontal direction), you know the vertical displacement to be 1.5 m downwards, and you know the vertical acceleration to be 9.8 m/s^2 downward. You need to use this information in the equations of motion in order to get the final vertical velocity and time of fall.

confidence assessment: 0

.................................................

......!!!!!!!!...................................

23:33:32

We analyze the vertical motion first. The vertical motion is characterized by initial velocity zero, acceleration 9.8 meters/second^2 and displacement 1.5 meters. Since the initial vertical velocity is zero the equation `ds = v0 `dt + .5 a `dt^2 becomes `ds = .5 a `dt^2, which is easily solved for `dt to obtain `dt = `sqrt( 2 `ds / a) = `sqrt( 2 * 1.5 m / (9.8 m/s^2) ) = .54 sec, approx., so the object falls for about .54 seconds.

The horizontal motion will therefore last .54 seconds. Since the initial 6 meter/second velocity is in the horizontal direction, and since the horizontal velocity is unchanging, the object will travel `ds = 6 m/s * .54 s = 3.2 m, approximately.

......!!!!!!!!...................................

RESPONSE -->

I have a hard time understanding this idea. i will study this more!!

We analyze the vertical motion first. The vertical motion is characterized by initial velocity zero, acceleration 9.8 meters/second^2 and displacement 1.5 meters. Since the initial vertical velocity is zero the equation `ds = v0 `dt + .5 a `dt^2 becomes `ds = .5 a `dt^2, which is easily solved for `dt to obtain `dt = `sqrt( 2 `ds / a) = `sqrt( 2 * 1.5 m / (9.8 m/s^2) ) = .54 sec, approx., so the object falls for about .54 seconds.

The horizontal motion will therefore last .54 seconds. Since the initial 6 meter/second velocity is in the horizontal direction, and since the horizontal velocity is unchanging, the object will travel `ds = 6 m/s * .54 s = 3.2 m, approximately.

self critique assessment: 3

.................................................

......!!!!!!!!...................................

23:38:12

`q004. An object whose initial velocity is in the horizontal direction descends through a distance of 4 meters before it strikes the ground. It travels 32 meters in the horizontal direction during this time. What was its initial horizontal velocity? What are its final horizontal and vertical velocities?

......!!!!!!!!...................................

RESPONSE -->

I need to get help with these types of situations. I have no idea.

What do you know about the vertical motion? Which of the variables v0, vf, `dt, a and `ds do you know? Which equation(s) would you then use to solve the vertical motion?

confidence assessment: 0

.................................................

......!!!!!!!!...................................

23:39:40

We analyze the vertical motion first. The vertical motion is characterized by initial velocity zero, acceleration 9.8 meters/second^2 and displacement 4 meters. Since the initial vertical velocity is zero the equation `ds = v0 `dt + .5 a `dt^2 becomes `ds = .5 a `dt^2, which is easily solved for `dt to obtain `dt = `sqrt( 2 `ds / a) = `sqrt( 2 * 4 m / (9.8 m/s^2) ) = .9 sec, approx., so the object falls for about .9 seconds.

The horizontal displacement during this .9 second fall is 32 meters, so the average horizontal velocity is 32 meters/(.9 second) = 35 meters/second, approximately.

The final vertical velocity is easily calculated. The vertical velocity changes at a rate of 9.8 meters/second^2 for approximately .9 seconds, so the change in vertical velocity is `dv = 9.8 m/s^2 * .9 sec = 8.8 m/s. Since the initial vertical velocity was zero, final vertical velocity must be 8.8 meters/second in the downward direction. The final horizontal velocity is 35 meters/second, since the horizontal velocity remains unchanging until impact.

......!!!!!!!!...................................

RESPONSE -->

We analyze the vertical motion first. The vertical motion is characterized by initial velocity zero, acceleration 9.8 meters/second^2 and displacement 4 meters. Since the initial vertical velocity is zero the equation `ds = v0 `dt + .5 a `dt^2 becomes `ds = .5 a `dt^2, which is easily solved for `dt to obtain `dt = `sqrt( 2 `ds / a) = `sqrt( 2 * 4 m / (9.8 m/s^2) ) = .9 sec, approx., so the object falls for about .9 seconds.

The horizontal displacement during this .9 second fall is 32 meters, so the average horizontal velocity is 32 meters/(.9 second) = 35 meters/second, approximately.

The final vertical velocity is easily calculated. The vertical velocity changes at a rate of 9.8 meters/second^2 for approximately .9 seconds, so the change in vertical velocity is `dv = 9.8 m/s^2 * .9 sec = 8.8 m/s. Since the initial vertical velocity was zero, final vertical velocity must be 8.8 meters/second in the downward direction. The final horizontal velocity is 35 meters/second, since the horizontal velocity remains unchanging until impact.

self critique assessment: 2

................................................."

See my notes. You should probably work through at least some of these problems again. You might want to submit a copy of that last problem along with my questions, inserting your answers and/or questions (mark insertions by &&&&).