Height Question: Projectile launched from a table

In summary: If down is positive, then the displacement is positive but the gravitational acceleration is negative.
  • #1
fandomgeek_394
8
0

Homework Statement


A toy car rolls off of a table at an initial angle of 0 degrees and an initial velocity of 2.81 m/sec. The ball hits the floor 1.55 m (horizontally) from the edge of this table. How tall is the table?

Homework Equations

The Attempt at a Solution


So far I have:
Vo=(2.81 m/sec) * cos(0 degrees)=2.81 m/sec
Delta x= vot + one half at^2
1.55m=(2.81 m/sec) times t plus one half times (0) times t^2
t=1.55 m/2.81 m/sec=0.55 sec
Vo=(2.81 m/sec) times sin(0 degrees)=0 m/sec
Delta x=vot plus one half at ^2
Delta x= (0 m/sec) times (0.55) plus one half times (-9.8 m/sec) times (0.55 sec)^2=

The result I ended up getting was -1.48225 when I was done; I feel I know I must have made a mistake at some point, as the answer shouldn't have turned up negative. Someone I asked briefly on another site came up with the answer 1.488m for the problem; I'm just not quite sure what I got off. Could someone help me figure this one out please? I feel I'm close, but off somewhat. Thanks for the help & the patience, guys.
Really do want to learn, and whatever help you can give me in making sure I get this problem right would be very appreciated. :)
 
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  • #2
The formula you used for the vertical motion gives you the displacement at time t. You took up as positive, making g negative. In falling to the floor, would you expect the displacement to be positive or negative?
 
  • #3
Negative? I feel kind of ridiculous right now, but I still don't quite understand... Do you think you could tell me what lines in my data are off and what exactly in them I need to change? I think that would help me.
 
  • #4
Was it the -9.8 in the problem that I got wrong? I just noticed that when I make that positive instead of negative, I get the positive answer.
 
  • #5
fandomgeek_394 said:
Was it the -9.8 in the problem that I got wrong? I just noticed that when I make that positive instead of negative, I get the positive answer.
You have to decide whether to make up positive or down positive. It does not matter so long as you are consistent. If up is positive then both the gravitational acceleration and the displacement are negative.
 

1. What factors affect the height of a projectile launched from a table?

The height of a projectile launched from a table is affected by the initial velocity, angle of launch, and the force of gravity.

2. How does the angle of launch affect the height of a projectile?

The angle of launch affects the height of a projectile by determining the vertical and horizontal components of the initial velocity. A higher angle of launch will result in a higher vertical velocity, leading to a higher maximum height.

3. Does air resistance affect the height of a projectile launched from a table?

Yes, air resistance can affect the height of a projectile launched from a table. It can decrease the maximum height by slowing down the projectile as it travels through the air.

4. Is there a maximum possible height for a projectile launched from a table?

Yes, there is a maximum possible height for a projectile launched from a table. This is determined by the initial velocity, angle of launch, and force of gravity. Once the projectile reaches its maximum height, it will begin to fall back down due to the force of gravity.

5. How can we calculate the height of a projectile launched from a table?

The height of a projectile launched from a table can be calculated using the equation h = (v^2 * sin^2θ)/(2g), where h is the maximum height, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity (9.8 m/s^2).

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