Motion 2 problems - Tossing hay bales and baseballs

[blackraven]

Motion 2 problems -- Tossing hay bales and baseballs

Homework Statement

1. A hay-baling machine throws each finished bundle of hay 2.0 m up in the air so it can land on a trailer waiting 4.7 m behind the machine.

(a) What must be the speed with which the bundles are launched?

2. A baseball is popped up, remaining aloft for 6.3 s before being caught at a horizontal distance of 83 m from the starting point. What was the launch angle?

Homework Equations

1. x = 1/2at^2 +vot +x0
x-xo = d

2. vx = cos*vo
vy = sin*vo

The Attempt at a Solution

1. I used the distance and plugged it into the first equation but it is the wrong answer I believe.
2. I know that in the end I have to divdide vy by vx and take the arctan of that but I do not understand how to find vy and vx. Can someone explain to me step by and step and what that means?

 

[Saitama]

The Attempt at a Solution

1. I used the distance and plugged it into the first equation but it is the wrong answer I believe.
2. I know that in the end I have to divdide vy by vx and take the arctan of that but I do not understand how to find vy and vx. Can someone explain to me step by and step and what that means?

Let's first talk about the vertical motion. At the maximum height, velocity is zero. Initially, the vertical velocity is vsinθ (a component of the initial velocity making an angle θ with the ground). You have initial velocity, final velocity, displacement and the acceleration.
Can you form an equation now?

 

[xlava]

This is going to sound like weird advice, but you're not thinking about the problem right. Don't think "I know that in the end I have to..." Just work through it.

Your equations are sound. Let's start with this: you know the maximum height right? What can you find with that if you know the acceleration of gravity?

 

[azizlwl]

1

Homework Equations

1. x = 1/2at^2 +vot +x0
x-xo = d

2. vx = cos*vo
vy = sin*vo

ISEE Method

1. Identify
a) Only one object - the hay bale
b) The object doing 2 works. Going in horizontal and verical motion.

2. Select
y=y₀+v_y0t_y+(1/2)a_yt_y²
x=x₀+v_x0t_x+(1/2)a_xt_x²

Since it involves only one object,
t_y=t_x

3. Execute
4. Evaluate

 

[Nickie]

For the first problem, we can use the equation x-x0 = d, where x is the final position, x0 is the initial position, and d is the distance. We know that the final position is 4.7 m behind the machine and the initial position is 0 m. So, we can plug in these values and solve for d:

x-x0 = d
4.7 m - 0 m = d
d = 4.7 m

This means that the hay bale must be launched with a speed that will make it travel a distance of 4.7 m in order to land on the trailer.

For the second problem, we can use the equations vx = cos*vo and vy = sin*vo to find the launch angle. We know that the horizontal distance traveled is 83 m and the time the ball was in the air is 6.3 s. So, we can use the equation vx = d/t to find the horizontal velocity:

vx = d/t
vx = 83 m/6.3 s
vx = 13.2 m/s

Now, we can use the equation vy = sin*vo to find the vertical velocity. We know that the ball was caught at the same height it was launched from, so the final vertical position is the same as the initial vertical position:

vy = sin*vo
0 m/s = sin*vo
sin*vo = 0

This means that the initial vertical velocity must be 0 m/s. Now, we can use the equation vx = cos*vo to find the launch angle:

vx = cos*vo
13.2 m/s = cos*vo
cos*vo = 13.2 m/s

We can use a calculator to find the inverse cosine of 13.2 m/s, which is approximately 82.3 degrees. So, the launch angle of the baseball was approximately 82.3 degrees.