Projectile motion and circular motion questions

In summary, 1) The linear speed of the blade tip is 530rev/min. 2) The radial acceleration of the blade tip is expressed as a multiple of the acceleration of gravity, g = 3.6 m/s2.
  • #1
babbagee
74
0
Ok I have two questions which I am stuck on. I just need some hints.

1.)An airplane is flying with a velocity of 90.0 m/s at an angle of 23.0m\s above the horizontal. When the plane is a distance 115 m directly above a dog that is standing on level ground, a suitcase drops out of the luggage compartment.

q.)How far from the dog will the suitcase land? You can ignore air resistance

For this one I think I have to calculate the time it takes for the suitcase to hit the ground. And then I can use d=vt to calculate the distance away from the dog. But i am having a problem with the intial velocity in the y direction. When the suitcase falls off the plane its intial velocity is not zero right. Its inital velocity will be the same as the plane right.

2.)A model of a helicopter rotor has four blades, each of length 3.60 m from the central shaft to the blade tip. The model is rotated in a wind tunnel at a rotational speed of 530rev/min.
q1.)What is the linear speed of the blade tip?
q2.)What is the radial acceleration of the blade tip expressed as a multiple of the acceleration of gravity, g?

Really don't know where to start out on this one, just point me in the right direction.

Thanks
 
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  • #2
1) Right general idea. Split the velocity of the plane into horizontal and vertical components and you're pretty much set to go.

2) For part 1, think about how far the blade tip has to go to complete one revolution, then how long it takes for it to complete said revolution.

For part 2, would it help if I pointed out that that's the centripetal acceleration?
 
  • #3
Hey thanks,

For the first question I was using 115 m instead of negative. Thats why i kept getting it wrong.

And for question 2, I didn't think about the circumference until you stated it. And i figured out the acceleration as well.
 
  • #4
what are the answers to these questions?
 
  • #5
for your questions! It's great to see that you are thinking deeply about these problems and trying to come up with a solution.

For the first question, you are on the right track. To calculate the distance the suitcase will land from the dog, you will need to find the time it takes for the suitcase to fall. This can be done by using the equation h= 1/2gt^2, where h is the height, g is the acceleration due to gravity (9.8 m/s^2) and t is time. Since the initial velocity in the y direction is 90*sin(23), you can use this value to find the time it takes for the suitcase to fall 115m. Once you have the time, you can use the equation d=vt to find the distance from the dog.

For the second question, you will need to use the formula v=ωr, where v is the linear speed, ω is the angular velocity (in radians per second), and r is the radius (blade length in this case). You are given the rotational speed in revolutions per minute, so you will need to convert it to radians per second. Once you have the linear speed, you can use the formula a=v^2/r to find the radial acceleration. Remember to express the acceleration as a multiple of g by dividing it by 9.8 m/s^2.

I hope this helps you get started on these problems. Remember to always check your units and use the correct formulas for each type of motion. Good luck!
 

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 called a parabola due to the combination of horizontal and vertical motions.

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

The range of a projectile can be calculated using the equation R = (v^2sin2θ)/g, where R is the range, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

3. What is circular motion?

Circular motion is the movement of an object along a circular path at a constant speed. It is characterized by a centripetal force, which is the force acting towards the center of the circle, and a centrifugal force, which is the force acting away from the center.

4. How is centripetal force related to circular motion?

Centripetal force is the force that keeps an object moving in a circular path. It is equal to the mass of the object multiplied by its velocity squared, divided by the radius of the circle it is moving in.

5. What is the difference between centripetal force and centrifugal force?

Centripetal force is the force that keeps an object moving in a circular path, while centrifugal force is the apparent outward force that an object experiences as it moves in a circular path. Centrifugal force is not a real force, but rather a result of the object's inertia.

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