Projectile motion - have i done this correctly?

In summary, the conversation was about a problem involving a ball being kicked from a slope and when it will hit the slope again. The solution involved finding the components of distance traveled and using the equation tan(a)=Sy/Sx to find the time at which the ball will hit the slope. The conclusion was that the approach was correct and the resulting equation was a function of the initial velocity and the angle of the slope.
  • #1
Mglafas
3
0
I'm unsure whether I have done the following problem correctly :)

Homework Statement



A ball is kicked at from the slope as shown.
When will the ball hit the slope?

http://img90.imageshack.us/img90/8084/slopevi0.th.jpg

Homework Equations



The distance traveled can be expressed in two components:
Sx=vt
Sy=0.5gt^2

The displacement compontents can also be expressed in terms of tan(a)
tan(a)=Sy/Sx

The Attempt at a Solution



Substituting we get:
Sy=Sx*tan(a)
0.5gt^2=vt*tan(a)
0.5gt=v*tan(a)
t=[2v*tan(a)]/g

Is this correct?
 
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  • #2
Your approach is looks sound to me. The idea is you want to find the components x and y that match the slope of the ramp.
 
  • #3
Mglafas said:
Substituting we get:
Sy=Sx*tan(a)
0.5gt^2=vt*tan(a)
0.5gt=v*tan(a)
t=[2v*tan(a)]/g

Is this correct?

That looks fine.

What you apparently developed is the equation for angle of the ball, as a function of t, from some point down the slope, and by setting the angle of tan to θ, that's where it hits and you have the value for the time now as a function of Vo and θ. Good job.
 
Last edited:

FAQ: Projectile motion - have i done this correctly?

1. What is projectile motion?

Projectile motion is the motion of an object through the air that is influenced by the force of gravity. It follows a curved path, known as a parabola, and is affected by the initial velocity, angle of projection, and the acceleration due to gravity.

2. How do you calculate the displacement of a projectile?

The displacement of a projectile can be calculated using the formula d = v0 * t + 1/2 * a * t2, where v0 is the initial velocity, t is time, and a is the acceleration due to gravity.

3. What is the difference between horizontal and vertical velocity in projectile motion?

The horizontal velocity remains constant throughout the motion, while the vertical velocity changes due to the acceleration of gravity. This means that the horizontal displacement is directly proportional to the time, while the vertical displacement is proportional to the square of the time.

4. How does the angle of projection affect projectile motion?

The angle of projection determines the initial direction of the projectile's motion. A higher angle will result in a longer flight time and a greater horizontal displacement, while a lower angle will result in a shorter flight time and a smaller horizontal displacement.

5. What factors can affect the accuracy of projectile motion calculations?

The accuracy of projectile motion calculations can be affected by air resistance, which can vary depending on the shape and size of the object. Other factors include the initial velocity, angle of projection, and the precision of the measurements used in the calculations.

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