In this problem, let\'s model air resistance by having a projectile in the air l

Question

In this problem, let's model air resistance by having a projectile in the air launched at 45 degrees above +x axis with an x acceleration that is smaller as time goes forward since on average the projectile slows down. Take ax= -aoe-t/t* where t* = total time of trip.

First, determine the equation for y(t) for a regular projectile (ax=0) launched with speed of 10m/s at an angle of 45 degrees.
Now turn on the air resistance in the model by setting k to be some positive constant such that the maximum x acceleration is 40% gravity; determine the value of ao

Explanation / Answer

y(t) will not be affected due to acceleration in the x direction, as it has no component along the y direction. Hence, y(t) = 10/root(2) * t + 1/2 * g * t^2 = 7.07 t + 4.5 t^2 Now, a = d2x/dt2 On integrating, x(t) = (t/t*)^2 x ao e^-t/t* Using the above two functions, we can find r(t) = x(t) i + y(t) j

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.