A hot-air balloon is rising straight up at a constant speed of 7.0m/s. When the

Question

A hot-air balloon is rising straight up at a constant speed of 7.0m/s. When the balloon is 12.0 m above the ground, a gun fires a pellet straight up from ground level with an initial speed of 30.0m/s. Along the paths of the balloon and the pellet, there are two places where each of them has the same altitude at the same time. How far above ground are these places? The three objects are connected by strings that pass over massless, friction-free pulleys. The objects move, and the coefficient of kinetic friction between the middle object and the surface of the table is 0.100. (a) What is the acceleration of the three objects? (b) Find the tension in each of the two strings.

Explanation / Answer

1)

s = ut

balloon height from ground(s1) = 12 + 7t

pellet height from ground by

s = ut + 1/2gt^2

s2 = 30t - 1/2 x 9.8 x t^2

By s1 = s2

12 + 7t = 30t - 4.9t^2

4.9t^2 - 23t + 12 = 0

t = [-(-23) +/- sqrt{(-23)^2 - 4 x 4.9 x 12}] / [2 x 4.9]

t = [23+/-17.14] / 9.8

t = 0.60 or 4.10 sec

s1 = [12 + 7 x 0.60] or [12 + 7 x 4.10] m

s1 = 16.20 or 40.70 m

2)

F(net) = ma

m1g - m2g - m3g = (m1 + m2 + m3)a

9.81(25 - 10 - 0.100(80)) = (25 + 10 + 80)a

a = 0.597 m/s^2 ===ANS a)

T = m1(g - a)

T = 25(9.81 - 0.597)

T = 230 N === ANS b)

T = m2(g + a)

T = 10(9.81 + 0.597)

T = 98.70 N === ANS c)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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