Kinematics: Traveling in an arc

In summary, the conversation discusses a problem involving a cannonball being fired from a cliff of height 45m with a velocity of 30m/s. The time taken for the ball to reach the ground is calculated to be 3.0 seconds using the formula s=vt+0.5at^2. The range and velocity of the ball as it touches the ground are then discussed, with the understanding that velocity in two-dimensional motion can be resolved into horizontal and vertical components. The final velocity of the ball as it touches the ground is approximately 42m/s, with a horizontal distance of 90m and a vertical velocity of 30m/s. The conversation also mentions the use of trigonometry and vector concepts in
  • #1
zesi
10
0

Homework Statement


Consider a cannonball being fired with a velocity of 30m/s from a cliff of height 45m.

http://imgur.com/OCMNEPv

(a) Calculate the time taken for the ball to reach the ground.

(b) Calculate the range of the motion.

(c) Calculate the horizontal velocity, vertical velocity, and the velocity of the cannon ball as it touches the ground.

Homework Equations



4 kinematics formula.

The Attempt at a Solution



(a) using s=vt+0.5at^2
I found out t=3.0sI am having a hard time with (b) and (c) because it is traveling in an arc. I am not sure how I should proceed.

(b) I don't think I can assume the calculation that it travels in a straight line down, then use trigonometry to find the range. What other ways can I think of?

(c) If I use "v(f) = v(i) + at" then it will the final velocity will be 60m/s, assuming acceleration (due to gravity) = 10m/s^2. However is this 60m/s the vertical velocity or the velocity as it touches the ground?

From my understanding v(f) = 60m/s is the vertical velocity. Once I have the range (horizontal distance) I can use it to find the horizontal velocity. Using vector concept, taking
vertical velocity - horizontal velocity
= velocity as it touches the ground.

I am having a hard time figuring out the horizontal distance.

Correct me if I am wrong.
Which concept am I not getting it? Hope someone can help me. Thank you.
 
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  • #2
Have you dealt with projectile motion questions in the past?
 
  • #3
Hi PWiz. No I have not learned projectile motion. How should I understand the concept?

Thanks
 
  • #4
You will first have to understand that velocity in two dimensional motion can always be resolved into it's x and y components. If I throw a ball with an initial velocity ##u## into the air at an acute angle theta from the surface, the ball takes an approximately curved (parabolic) path. Can you give me expressions for the two components(x and y) of the velocity in terms of ##u## and theta right at the beginning?
 
  • #5
Ohhh! I keep thinking because it is an arc and didn't break down into it's horizontal and vertical direction. Here is what I did. Please correct me if I am wrong.

I understand that horizontal distance is constant = 30m/s

So I know the time taken is 3.0sec. 30x3 = 90m.
Therefore, horizontal distance = 30m

Now I can I use v(f) = v(i) + at to find my vertical velocity. Since v(i) = 0m/s
I get 30m/s.

Using vector concept and pythagoras theorem,
final velocity as it touches the ground
= sqrt[(horizontal velocity)^2 + (veritcal velocity)^2]
approximately 42m/s.

I feel makes sense. Am I wrong in ny concept? Thank you.
 
  • #6
zesi said:
I understand that horizontal distance is constant = 30m/s
I think you mean the magnitude of the horizontal velocity is 30 m/s .
zesi said:
horizontal distance = 30m
I take it that this is also a typo; you've correctly evaluated the distance to be approximately 90m previously.

Other than these two things, your answer (and understanding) is perfectly fine.
 
  • #7
Oh so sorry! Yes I got.

magnitude of Horizontal velocity= 30m/s.

Horizontal distance = 90m

Sorry made a very bad typo.

Thank you for the confirmation PWiz
 

What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.

What is traveling in an arc?

Traveling in an arc refers to the motion of an object in which it follows a curved path rather than a straight line. This type of motion is commonly seen in circular or projectile motion.

What is the difference between linear and angular velocity?

Linear velocity is the rate of change of an object's position in a straight line, while angular velocity is the rate of change of an object's angular position around a fixed point.

How is acceleration related to traveling in an arc?

Acceleration in traveling in an arc is related to the change in the direction of the velocity of an object. In circular motion, the acceleration is constantly changing due to the constantly changing direction of the object's velocity.

What is the centripetal force?

The centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is responsible for constantly changing the direction of the object's velocity in circular motion.

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