Projectile motion of a snowmobile

[getty102]

Homework Statement

The snowmobile is traveling at 10m/s when it leaves the embankment at A. The angle that the snowmobile leaves its elevated jump is 40 degrees. Determine the time and flight from A to B and the range R of the trajectory.
The slope of the mountain is a 3-4-5 triangle.

Homework Equations

y=y_0+10sin40(t)-.5(9.81)t^2
R=10cos40(t)

The Attempt at a Solution

I wasn't sure how to get the height, range, and time(in the air) using only the equations of projectile motion.

 

[omoplata]

I am guessing from what I read that B is either up a mountain from A or down a mountain, and the slope of the mountain is in the form of a 3:4:5 right angled triangle.

Is B higher than A, or lower than A?

Is y/R equal to 3/4, or is it equal to 4/3 ?

Without knowing these the question can't be answered. Is there a diagram that comes with this problem?

 

[getty102]

You are correct, the point A starts at an elevated position while point B is at a lower position. The 3-4-5 triangle has its 3 side underneath point A and the 4 side would be considered the Range.

 

[omoplata]

OK, then if you consider the motion upwards to be positive, since the vertical position of the projectile ends up lower than it's starting vertical position (i.e. since it falls), your first equation should change to this.

-y=y_0+10sin40(t)-.5(9.81)t^2

Your second equation is correct for the range,

R=10cos40(t)

Also,

y_0 = 0

From the sides of the 3:4:5 triangle we can get the following relation,

y/R = 3/4

These four equations are all you need to find y, R and t.

 

[rwisz]

However, assuming that the snowmobile starts at the same level as point A and that the slope of the mountain is a 3-4-5 triangle, we can use the Pythagorean theorem to find the height at point A. The height would be 3/4 of the hypotenuse, so h=7.5m.

Using the equation y=y_0+10sin40(t)-.5(9.81)t^2, we can solve for t by setting y=0 because the snowmobile will land at the same height as it started.
0=7.5+10sin40(t)-.5(9.81)t^2
Solving for t, we get t=1.3s.

To find the range, we can use R=10cos40(t). Plugging in our value for t, we get R=8.1m. Therefore, the snowmobile will travel a horizontal distance of 8.1m before landing at point B.

In conclusion, the time of flight for the snowmobile is 1.3 seconds and the range is 8.1 meters. However, it's important to note that these values may vary depending on the actual height and slope of the mountain in the given scenario. More information and measurements would be needed to accurately determine the time and range of the snowmobile's projectile motion.