Find Slope of Run to Reach 40 m/s in 30 Seconds

[Dejahboi]

Homework Statement

Olympic skeleton sled racers can reach speeds of 40 m/s. Find the slope needed to reach that speed after a 30 second run, neglecting friction.

Homework Equations

F=ma

The Attempt at a Solution

I honestly burnt myself out from the previous question on my homework where instead I had to find the final velocity from a given angle and frictionless slope. Just this time I'm solving for the angle.

I assume ( using previous work) :

Time/ 9.81 = sinx ? idk... :/

 

[Sourabh N]

Questions you should ask yourself:
1. What is speeding the sled?
2. How much is the acceleration?
3. Given this acceleration, what will the velocity be after 30 seocnds if sled starts from rest?

Which of these can you answer?

 

[Dejahboi]

Well I understand since the speed in this problem is defined by gravity so 9.81 m/s^2?

 

[Sourabh N]

Well I understand since the speed in this problem is defined by gravity so 9.81 m/s^2?

You're right in thinking that gravity is accelerating the sled, but the sled is not falling vertically downwards. It's going down an incline. What is the accelerations of an object going down an incline of slope θ?

 

[Dejahboi]

*sigh* lol i feel like there's lots of light on me... I'm assuming I have to think in cosine since it's going down along the x-axis (sorry thinking calc. terms).

 

[Sourabh N]

I would suggest drawing a free body diagram. Are you familiar with those?

If not, read that section from your textbook. Here's an online resource.