Projectile being launched off a table at an angle?

[megmar95]

Homework Statement

We did an experiment where we launched a ball off a table at an initial velocity of 1.80 m/s, at an angle of 10 degrees. We measured the distance in the x-axis the ball traveled 0.743 m. Using this information, we are supposed to calculate a predicted value for the distance in the y-axis (initial height). Since we did the experiment, we have an experimental value of 1.12 m for the height, but my teacher wants us to calculate a predicted value for initial height and compare using absolute % error ((predicted - experimental) / experimental).

Homework Equations

vix = (vi)cos(10)
vfy=(vi)sin(10)
ax = 0
ay= -9.81
t = ?
dx= 0.743 m
dy = ?

The Attempt at a Solution

I calculated vix to be 1.773 m/s and viy to be 0.3125667 m/s. I'm unsure how to calculate time, and also am unsure if there is a vi for y-axis (my teacher said I did the question wrong because I used dy= vit + 1/2at^2 and canceled out vit because I believed vi was 0 but the ball is being launched so there is a vi for y).

 

[voko]

The equation you used wrongly is OK, just use it correctly. Since ##v_{iy}## is not zero, as you said, do not set it to zero.

 

[tiny-tim]

hi megmar95! welcome to pf!

Using this information, we are supposed to calculate a predicted value for the distance in the y-axis (initial height).

the initial height is zero

do you mean maximum height?

(and is the table flat? and is the ball landing on the table again, or on the floor?)

… am unsure if there is a vi for y-axis (my teacher said I did the question wrong because I used dy= vit + 1/2at^2 and canceled out vit because I believed vi was 0 but the ball is being launched so there is a vi for y).

yes, v_i is at an angle, so v_iy = v_isin10°

 

[megmar95]

Ya I meant the distance traveled by the ball in the y-axis altogether (range)
The ball was launched off the end of a ramp angled at 10 degrees placed on top of a flat table at the very edge of it, and landed on the floor.
I tried using the (vi)sin(10) and plugged it into the equation d=vit+1/2at^2, so d= (0.3125)(0.419) + 1/2(9.81)(0.419)^2 and I got an answer of 0.992 m for predicted height. Afterwards I used the % error equation, and got a percent error of 11.4%, does that sound correct?

 

[HalfLostAndSearching]

I would advise you to first clarify with your teacher what they mean by "predicted value for initial height." Are they asking for the initial height at which the projectile was launched, or are they asking for the predicted height at a certain time after launch?

To calculate the initial height, you can use the equation dy = viy*t + 1/2*ay*t^2, where viy is the initial velocity in the y-direction (0.3125667 m/s in your case) and ay is the acceleration due to gravity (-9.81 m/s^2). You can solve for t using the information you have, such as the distance traveled in the x-direction and the initial velocity in the x-direction.

If your teacher is asking for the predicted height at a certain time after launch, you can use the equation y = viy*t + 1/2*ay*t^2, where y is the height at a certain time t and viy and ay are the same as before. You can plug in the time t and solve for y.

In terms of the initial velocity in the y-direction (viy), it is not necessarily 0. It depends on the angle at which the projectile was launched. In this case, you correctly calculated it to be 0.3125667 m/s. If your teacher is saying that you did the question wrong because you assumed viy to be 0, then you should clarify with them what they mean and ask for guidance on how to approach the question.

In terms of calculating time, you can use the equation dx = vix*t, where dx is the distance traveled in the x-direction and vix is the initial velocity in the x-direction (1.773 m/s in your case). Again, you can solve for t using the information you have.

I would also suggest double-checking your calculations and units to ensure accuracy. And when comparing your predicted and experimental values, make sure to use the absolute value of the difference in order to get a positive percentage error.

Overall, I would recommend discussing any confusion or questions with your teacher and seeking their guidance in completing the question accurately.