a balloonist releases a ballest bag from a balloon rising at 40m/s at a time when a balloon is 100m above the ground ,if g=10m/s then the bag reaches to ground in
S= Ut+1/2at2
-100=40t-5t2
Solving it
t= 10
To find the time it takes for the ballast bag to reach the ground, we can use the formula:
Time = Distance / Velocity
Given:
Initial velocity of the balloon (u) = 40 m/s
Height of the balloon (h) = 100 m
Acceleration due to gravity (g) = 10 m/s²
First, let's calculate the time it takes for the balloon to reach the ground:
Using the equation of motion for vertical motion, we have:
h = ut + (1/2)gt²
Solving for time (t), we get:
t = √(2h / g)
t = √(2 * 100 / 10)
t = √(20)
t = 4.47 seconds (approx)
Now, let's find the time it takes for the ballast bag to reach the ground after it is released.
Since the bag is released at the same height as the balloon, the time it takes for the bag to reach the ground will also be approximately 4.47 seconds.
To find the time it takes for the ballast bag to reach the ground from a balloon, you need to use the equations of motion.
In this scenario, the initial velocity (u) of the bag is 40 m/s upwards since it is released from a rising balloon. The acceleration (a) due to gravity is -10 m/s², which is negative because it acts downwards. The initial displacement (s) of the bag is 100 m since it is 100 m above the ground.
The equation that relates these variables is:
s = ut + (1/2)at²
In this equation, s represents the displacement, u represents the initial velocity, t represents the time, and a represents the acceleration.
We want to find the time it takes (t) for the bag to reach the ground, which means the displacement (s) will be equal to 0. So, we can rewrite the equation as:
0 = 40t + (1/2)(-10)t²
Simplifying this equation, we get:
-5t² + 40t = 0
Next, we can factor out common terms to solve for t:
t(-5t + 40) = 0
This equation has two solutions: t = 0 and -5t + 40 = 0.
Since time cannot be negative, we discard the second solution. Thus, t = 0.
Therefore, it takes 0 seconds for the ballast bag to reach the ground.
time of flight: h=vo*t-1/2 g t^2
vo=40
g= 9.8
h=100 solve for time t.
you will need to use the quadratic equation.