A hot air balloon is rising upward with a constant speed of 15 m/s. When the balloon is 2 m above the ground, the balloonist accidentally drops a compass over the side.
a.) How much time elapses before it hits the ground?
1.62882 s ?
b.) What is its speed just before it hits the ground?
9.8 m/s ??
c.) How high above the ground is the balloon when the compass hits the ground? 2 m??
2007-02-15 16:21:27 · 4 answers · asked by soccerjock 2 in Science & Mathematics ➔ Physics
Using
x = ut + ½ at² (taking upwards to be positive)
with the values a = g = -9.8 m/s², u = 15 m/s, and x = -2 m (for acceleration, a, time, t, initial speed, u, and displacement from origin, x).
Plugging in these values we get a quadratic in t,
4.9 t² - 15t - 2 = 0
Solving by the quadratic equation and taking only the positive root we get
t ≈ 3.19 s.
The speed on impact, v, can then be obtained by
v = u + at,
giving
v ≈ -16.3 m/s.
For the balloon, the height, h, is given by
h = 2 + vt
where v is its speed, a constant 15 m/s, giving
h ≈ 49.8 m.
2007-02-15 16:46:50 · answer #1 · answered by Anonymous · 0⤊ 0⤋
At the exact moment that it is dropped, the compass is travelling at 15 m/s upward. It must first be slowed down by gravity (9.8 m/s^2) whch will take 1.53 seconds. At that time it will have climbed a bit: it is now at
2 m + (1/2)*9.8*(1.53^2) m
Meanwhile, the baloon has reached 2 m + 1.53*15 m
The compass will accelerate towards the ground at a rate of 9.8 m/s^s and needs to cover the distance found above.
d = (1/2)*9.8* t^2
find t and that's the time the compass needs to fall from its highest point.
It's speed at that time t is given by:
v = a*t (a = 9.8 and t is what you just found).
Since t is more than 1 second (in fact, it must be more than 1.53), then it hits the ground at a speed greater than 9.8 m/s.
Meanwhile the balloon continues to climb at 15 m/s. When the compass hits the ground, the balloon height is:
2 + 15*1.53 + 15*t
Therefore, the answer to your question is:
no
2007-02-15 16:34:10 · answer #2 · answered by Raymond 7 · 1⤊ 0⤋
How much of the date do girls expect the guys to pay? I have gone on a few dates and she always wants to pay. I do not mind paying but then when we get to the movies she wants to pay as well. I might let her buy some popcorn but then she likes to sprinkls stuff on it that tastes wierd. When we get to the bowling alley he wants to be the one who takes off and puts on her shows? I guess us guys will never get you girls. Ha Ha
2007-02-15 16:23:48 · answer #3 · answered by Anonymous · 0⤊ 1⤋
i dont know.
2007-02-15 16:23:58 · answer #4 · answered by jhon_doe20 2 · 0⤊ 1⤋