Projectile Motion of ice skater

In summary, the conversation discusses a stunt for an ice skating show where a skater must skate down a frictionless ramp at a 15° angle and launch off a short horizontal section to fly through the air and land smoothly on the ice. The conversation includes equations for finding the distance and velocity needed for the stunt, and suggests using force analysis and kinematic equations to determine the starting point on the ramp.
  • #1
sphykik
22
0

Homework Statement



You are planning a stunt to be used in an ice skating show. For this stunt a skater will skate down a frictionless ice ramp that is inclined at an angle of 15° above the horizontal. At the bottom of the ramp, there is a short horizontal section that ends in an abrupt drop off. The skater is supposed to start from rest somewhere on the ramp, then skate off the horizontal section and fly through the air a horizontal distance of 6.40 m while falling vertically for 3.80 m, before landing smoothly on the ice. How far up the ramp should the skater start this stunt?

Homework Equations





The Attempt at a Solution



I found, using the Pythagorean theorem, that the distance diagonally (the hypotenuse) is 7.44m, but I am kind of stuck there.

Thanks a lot for you help!
Damian
 
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  • #2
Start by finding how long it takes for an object to fall 3.8m vertically using gravitational accel. Then use that time to relate how fast she must be going to travel 6.4m in the time that you find. That is a start
 
  • #3
so, using d= vt + (5.)(a)(t*t) <---- that's t squared, sorry :)

i did 3.8 = (0)(t) + (.5)(9.8)(t*t)

and found t to be be .88s

then i did

6.4 = v(.88) + (.5)(9.8)(.88)

and got v to be 2.97m/s

so that means that the skater will have to be going 2.97m/s. it this correct so far?
 
  • #4
the "short horizontal section" in the problem implies that there will be no acceleration in the horizontal direction. So your second formula is wrong
 
  • #5
so it would just be d = vt

6.4 = v(.88)

= 7.27 m/s ?

thanks
 
  • #6
can someone explain where to go from here? thanks
 
  • #7
Try using energy analysis (PE and KE) to find how far up she needs to be to achieve that speed...
 
  • #8
im sorry, i don't think we have covered that yet in class. i tried to look it up online, but I am not really having any luck. is there any other way to solve?
 
  • #9
Use force analysis to find how fast an object accelerates down a ramp that is 15 degrees. after that just use normal kinematic equations to relate distance/velocity/acceleration
 

1. What is projectile motion in the context of an ice skater?

Projectile motion in the context of an ice skater refers to the motion of the skater as they move through the air while performing jumps or other movements. It is a combination of horizontal and vertical motion that is affected by gravity and the initial velocity of the skater.

2. How does the mass of the ice skater affect their projectile motion?

The mass of the ice skater does not affect their projectile motion. According to the principles of projectile motion, the mass of an object does not affect its horizontal or vertical motion. Therefore, a skater with a larger or smaller mass will still follow the same trajectory when performing jumps or movements.

3. What factors can affect the distance of an ice skater's jump?

The distance of an ice skater's jump can be affected by several factors, including the initial velocity of the skater, the angle at which they take off, and air resistance. The initial velocity determines how far the skater will travel horizontally, while the angle of takeoff and air resistance can affect the vertical distance of the jump.

4. How does the ice surface affect the projectile motion of an ice skater?

The ice surface can affect the projectile motion of an ice skater in several ways. A smoother ice surface will create less friction, allowing the skater to maintain their initial velocity for a longer period of time. On the other hand, a rougher ice surface can cause the skater to slow down more quickly, potentially affecting the distance of their jump. Additionally, the texture of the ice can affect how the skater's blades interact with the surface, potentially altering their trajectory.

5. How does the force of gravity impact the projectile motion of an ice skater?

The force of gravity is a crucial factor in the projectile motion of an ice skater. Gravity causes the skater to be pulled towards the ground, affecting their vertical motion. Without gravity, the skater would continue moving horizontally without ever falling back to the ground. The force of gravity also affects the speed at which the skater falls, which can impact the distance and duration of their jumps.

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