You stand at the top of a vertical cliff. At the top of the cliff are many palm

Question

You stand at the top of a vertical cliff. At the top of the cliff are many palm trees and you have fashioned one into a catapult. Using this catapult, you are able to launch coconuts at an angle of 30 with initial velocity of 68 f t/s. If the distance from the base of the cliff to the top of the tree (spot where object is released) is 120 feet, determine the following: a. Find the parametric equations for the motion of the coconut. b. When does the coconut hit the ground? c. How far from the base of the cliff does the coconut travel (horizontal distance)?

Explanation / Answer

a) parametric equation is given by

x(t) = vo cos theta t

= 68 cos 30 t

= 34 sqrt 3 t

y(t) = - 16t^2 + vo sin theta t + h

y(t) = -16t^2 + 34t + 120

b) coconut hits the ground then y(t) = 0

0 =  -16t^2 + 34t + 120

solving the equation for t

dividing the entire equation by -2

8t^2 - 17t - 60 = 0

applying quadratic formula

t = {-b+- sqrt (b^2 - 4ac ) } / 2a

t = { 17 +- sqrt ( 17^2 + 4*60*8)}/16

t = 4

so , coconut will hit the ground after 4 seconds

c) x(t) = 34 sqrt 3 (4)

= 235.56 feet

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

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