SeniorPhysics Graded Assignment Help-Horizontal/Vertical Displacement

[Elle1121]

Homework Statement

A student is rolling a baseball off the roof of their house into their backyard pool.The house is 20 feet tall, and they roll the baseball off the flat roof at speed of 3 m/s towards the pool. How long is the ball in the air and how far away is the distance the pool must be from the house so that the ball hits the water?

I'm just not sure which of the three equations below to use!

Homework Equations

Horizontal displacement at a constant velocity: Change in X=v(t)
Vertical displacement due to free fall: 1/2g(t^2)
Vertical velocity due to free fall: V=gt

The Attempt at a Solution

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I took a stab at it, and I got two seconds for the time and 20 feet for the distance. I'm pretty sure they're both wrong though. Thanks for the help!

 

[CWatters]

Can you show your working? For example how did you get 2s for the time to fall 12ft (6m) ?

 

[NascentOxygen]

Hi Elle1121. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

I'm just not sure which of the three equations below to use! [...]

Vertical displacement due to free fall: 1/2g(t^2)

The best advice is that you use the equation which is going to help you get the answer! Consider the equation

x = ½gt²

This has two variables, and if either is known you can use the equation to calculate the other variable. Is that going to help you here?

It seems that this problem statement mixes feet and meters, or is this your typing mistake?

 

[Elle1121]

Hi Elle1121. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif The best advice is that you use the equation which is going to help you get the answer! Consider the equation

x = ½gt²

This has two variables, and if either is known you can use the equation to calculate the other variable. Is that going to help you here?

It seems that this problem statement mixes feet and meters, or is this your typing mistake?

The problem mixes feet and meters on purpose; my teacher wants us to get used to converting them. Also, thank you so much for your help!

 

[HalfLostAndSearching]

Hello,

To solve this problem, we can use the equations of motion for constant velocity and free fall.

First, let's determine the horizontal displacement of the baseball. We can use the equation for constant velocity, Δx = v(t), where Δx is the horizontal displacement, v is the velocity, and t is the time. In this case, the velocity is given as 3 m/s and the horizontal displacement is the distance from the house to the pool, which we will call d. So, we have:

d = 3t

Next, let's determine the vertical displacement of the baseball. We can use the equation for free fall, Δy = 1/2gt^2, where Δy is the vertical displacement, g is the acceleration due to gravity (9.8 m/s^2), and t is the time. In this case, the initial vertical displacement is 20 feet since the baseball is being rolled off a 20-foot tall roof. We can convert this to meters to be consistent with the units of acceleration (m/s^2). So, we have:

Δy = 20 feet = 6.1 meters

Now, we need to find the time it takes for the baseball to reach the pool, which we will call t. To do this, we can use the equation for vertical velocity, v = gt, where v is the final vertical velocity and t is the time. In this case, the final vertical velocity is 0 m/s since the baseball will be at rest when it hits the water. So, we have:

0 = 9.8t

Solving for t, we get t = 2 seconds.

Therefore, the ball will be in the air for 2 seconds and the distance the pool must be from the house is 6.1 meters. This is the same answer that you got, so it looks like you were on the right track! Good job!