A water balloon is tossed straight up from the ground with initial speed vb. Aft

Question

A water balloon is tossed straight up from the ground with initial speed vb. After a time t1, an arrow is shot straight up at the water ballon with speed va. You may neglect the effects of air resistance in this problem.

(a) In the absence of the arrow being shot, what is the maximum height that the water balloon would reach?

(b) Find an expression for the speed at which the arrow must be shot so that it hits the water balloon at the balloon’s highest point. Is there a condition that must be satisfied by t1 so that this is possible? Briefly explain.

(c) Draw qualitatively correct graphs for yb(t) (position of water balloon) and ya(t) (position of arrow) on the same set of axes (y versus t). Please indicate your choice of origin and direction for positive ˆj (increasing y).

Explanation / Answer

a)

Vb = initial velocity of ballon at ground

Vfb = final velocity of ballon at highest point

h = maximum height reached

using the equation

Vfb2 = Vb2 - 2 g h

h = Vb2 /(2 g)

b)

tb = time taken by ballon to reach maximum height

using the equation

Vfb = Vb - gt

t = Vb/g

time taken by arrow = t - t1

Using the equation

Vfa = Va - g(t - t1 )

0 = Va - g(Vb/g) - t1 )

0 = Va - Vb + gt1

t1 = (Vb - Va) / g

condition : t1 <t

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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