Projectile Motion Physics Question

[neelyboy]

How do you know if velocity in the y direction is zero or nonzero? For instance, on page 28 of TBR physics section I, example 1.13 (what is the flight time for an object fired from a horizontal cannon at 57.5 m/s from a cliff that is 143 m above the ground below) the explanation says that there is no initial velocity in the y direction and thus v initial is zero. however, on page 29 equations are given for where, when an angle is involved, v initial y = v initial * sin theta. i thought, for projectile motion, initial velocity in the y direction was always zero. how do you know/when is v initial in the y direction nonzero? thanks.

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[muhali3]

Basically, if the projectile is being shot at a non-zero angle, it will have a y-velocity. Projectile motion problems usually do have an initial y-velocity...I don't know where you heard that they don't. Maybe you're thinking about free-fall.

In projectile motion, the y-velocity = vinitial x sin theta (as you said). If theta is zero degrees, then sin theta = zero, making the y-velocity zero. So only at a zero-degree and 180-degree angle will there be no y-velocity.

 

[neelyboy]

thanks for the quick reply. i think i am confusing projectile motion and free-fall... im confused because the example i cited said that the object was FIRED from a cliff 143 m above the ground. so does this mean projectile motion or free fall?? the solution states to treat it as if the object were dropped from rest from an elevation of 143 m. so what i dont get is that if something is fired, doesnt that mean projectile and thus why is the initial velocity zero? wouldn't it be nonzero since it is FIRED (likely at an angle although it is not specified??).

also, can you compare and contrast projectile motion and freefall for me in a quick summary? thanks a bunch im tired but want to get this down.

 

[muhali3]

thanks for the quick reply. i think i am confusing projectile motion and free-fall... im confused because the example i cited said that the object was FIRED from a cliff 143 m above the ground. so does this mean projectile motion or free fall?? the solution states to treat it as if the object were dropped from rest from an elevation of 143 m. so what i dont get is that if something is fired, doesnt that mean projectile and thus why is the initial velocity zero? wouldn't it be nonzero since it is FIRED (likely at an angle although it is not specified??).

also, can you compare and contrast projectile motion and freefall for me in a quick summary? thanks a bunch im tired but want to get this down.

I'm no expert, but free-fall to me is something being dropped or shot horizontally from a certain height. Free-fall is a type of projectile motion. So something being fired doesn't mean that it was shot at an angle. More simply, free-fall is something falling eek...the object will never gain any height during its motion.

You just need to do a bunch of practice questions and you'll begin to understand what they're asking for. Usually, if there's a cliff, it's a free-fall question.

If you need more clarification, I recommend you watch this at 33:20 (when he starts talking about projectile motion): http://www.wikipremed.com/course_videos.php?syl=01&video_code=010101_02

 

[whiteshadodw]

How do you know if velocity in the y direction is zero or nonzero? For instance, on page 28 of TBR physics section I, example 1.13 (what is the flight time for an object fired from a horizontal cannon at 57.5 m/s from a cliff that is 143 m above the ground below) the explanation says that there is no initial velocity in the y direction and thus v initial is zero. however, on page 29 equations are given for where, when an angle is involved, v initial y = v initial * sin theta. i thought, for projectile motion, initial velocity in the y direction was always zero. how do you know/when is v initial in the y direction nonzero? thanks.

initial velocity in the y direction IS equal to sin theta. when its completely horizontal, then theta is ZERO. sin 0 degrees is zero, thus, in this scenario, but it is completely horizontal, theta is ZERO. conversely, cos 0 degrees is 1. hence, v initial in the x-direction is 57.5 cos 0 = 57.5

for projectile motion:

initial velocity in y-direction is ALWAYS v0 * sin theta
initial velocity in x-direction is ALWAYS v0 * cos theta

if it is fired completely horizontally then theta (the angle made with the ground) = ZERO degrees
if it is fired completely vertically then theta (the angle made with the ground)= 90 degrees

 

[Rabolisk]

Free fall just means that gravity is the only force acting on an object. This means that acceleration is constant and downward, but it says nothing about the direction of motion or velocity.

 

[golgiapparatus88]

Look at the two cases separately. The horizontal velocity will affect the range but that's pretty much it. If you throw two objects, one at 5 m/s and another at 10 m/s, the range will be different by d=vt. Since there is no initial vertical velocity, you can set it to 0. There are bunch of equations allowing you to solve for time. My personal favorite is t = sqrt(2h/g). Double the answer to get the total flight time and plug into d=vt to compare your ranges.

 

[BerkReviewTeach]

im confused because the example i cited said that the object was FIRED from a cliff 143 m above the ground. so does this mean projectile motion or free fall?? the solution states to treat it as if the object were dropped from rest from an elevation of 143 m. so what i dont get is that if something is fired, doesnt that mean projectile and thus why is the initial velocity zero? wouldn't it be nonzero since it is FIRED (likely at an angle although it is not specified??).

The angle is specified in a way you must interpret. The exact wording of the question is "What is the flight time for a projectile fired from a horizontal cannon at 57.5 m/s from a cliff that is 143 m above the ground below?"

They key word is "horizontal" before cannon, which implies that the projectile is given only x-component speed at launch. In the y-direction it's the same thing as dropping the projectile straight down from rest. The point of the question is that when you distill away all of the extraneous information (x-speed for instance), it's a kinematics question that can be answered using the short cut method. Falling 125 m would take 5 seconds and falling 180 m would take 6 seconds, so the correct answer must be about midway between 5 and 6 seconds.