2 Dimensional Motion and Vectors Help

This can be done using the Pythagorean theorem: V = sqrt(Vx^2 + Vy^2)In summary, the conversation discusses a problem involving a person standing at the edge of a cliff and kicking a stone over with a speed of 18 m/s. The question is how long it takes for the stone to fall to the water and with what speed it strikes the water. The person attempting the problem found the time to be 3.26 seconds using the equation dy= 1/2gt^2, but was unsure of how to find the speed. It is determined that the speed can be found by using vector addition and the Pythagorean theorem, resulting in a speed of 36.889 m/s.
  • #1
janhen200
8
0

Homework Statement



A person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of 18 m/s. The cliff is 52 m above the water's surface. How long does it take for the stone to fall to the water? With what speed does it strike the water?

Homework Equations


The Attempt at a Solution



So far, I was able to figure out the time:

dy= 1/2gt^2 where g=9.81 m/s^2
52m= 1/2*9.81*t^2
t= 3.26 seconds

I thought it would be correct to use Vy=gt to find the speed at which the stone strikes the water, therefore being (9.81 m/s^2)(3.26 s)= 31.98 m/s. But when i checked the answer key and talked to the teacher, she said that the answer was 36.889 m/s, and I was wrong.

So can someone tell me what I'm doing wrong and how to find the speed at which the stone strikes the water?
 
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  • #2
You have only calculated the vertical component of the speed.

You need to do a vector addition of this with the horizontal component.
 
  • #3


I would like to provide some clarification and guidance on your attempt to solve this problem. First, it is important to note that this problem involves two-dimensional motion, as the stone is being kicked off a cliff and will fall in a curved path to the water below. In these types of problems, it is helpful to break down the motion into its x and y components.

To find the time it takes for the stone to fall to the water, you correctly used the equation d=1/2gt^2, with d representing the vertical displacement and g representing the acceleration due to gravity. However, it is important to note that in this equation, d represents the displacement from the initial position, not the total height. So, in this case, d would be 52m, but the stone also has an initial vertical velocity of 18 m/s, which will affect its total displacement.

To find the x component of the stone's motion, we can use the equation Vx=Vox, where Vx represents the horizontal velocity and Vox represents the initial horizontal velocity, which is 0 in this case since the stone is kicked straight off the cliff. Therefore, the stone's horizontal velocity remains constant at 0 m/s throughout its motion.

For the y component, we can use the equation Vy=Voy+gt, where Vy represents the vertical velocity, Voy represents the initial vertical velocity, and g is still the acceleration due to gravity. In this case, Voy is equal to 18 m/s, since the stone is kicked off the cliff with that initial velocity.

Now, to find the total time it takes for the stone to fall to the water, we can use the equation t=d/Vy, where t is the time, d is the total displacement, and Vy is the final vertical velocity. In this case, d=52m and Vy=0 m/s, since the stone will reach the water with a vertical velocity of 0 m/s. Plugging in these values, we get t=2.89 seconds.

To find the speed at which the stone strikes the water, we can use the equation V=square root of (Vx^2+Vy^2), where V is the total velocity and Vx and Vy are the horizontal and vertical components, respectively. In this case, Vx=0 m/s and Vy=-g*t (since the stone is accelerating downward due to gravity). Plugging in these
 

1. What is 2 dimensional motion?

2 dimensional motion refers to the movement of an object in two different directions, typically represented by the x and y axes in a coordinate system. This type of motion is commonly seen in projectile motion, where an object moves both horizontally and vertically at the same time.

2. What are vectors in 2 dimensional motion?

Vectors in 2 dimensional motion are quantities that have both magnitude and direction. They are represented by an arrow and can be added or subtracted to determine the overall displacement of an object. In 2 dimensional motion, vectors often have both x and y components.

3. How do you calculate the magnitude of a vector in 2 dimensional motion?

The magnitude of a vector in 2 dimensional motion can be calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the x and y components. This can also be represented as |v| = √(x^2 + y^2).

4. What is the difference between displacement and distance in 2 dimensional motion?

Displacement refers to the change in position of an object, taking into account its starting and ending points. It is a vector quantity and can be positive, negative, or zero. Distance, on the other hand, refers to the total length traveled by an object regardless of its starting and ending points. It is a scalar quantity and is always positive.

5. How does acceleration affect 2 dimensional motion?

Acceleration in 2 dimensional motion can affect an object's velocity and direction. If an object experiences a constant acceleration in one direction, it will have a changing velocity and therefore a changing direction. If the acceleration is in two perpendicular directions, the object will experience a curved path and will constantly change its direction of motion.

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