a balloon starts rising from the ground, vertically upwards, uniformaly at a rate of 1m/s. At the end of 4 seconds a body was released from the balloon. Calculate the time taken by the realeased body to reach the ground. Take g=10m/s^2
To solve this problem, we need to consider the motion of both the balloon and the body separately.
The balloon is rising vertically upwards at a rate of 1 m/s. This means its velocity is constant at 1 m/s, and we can assume it continues to rise at this rate until the body is released. We also know that the acceleration due to gravity is g = 10 m/s^2.
After 4 seconds, the body is released from the balloon. At this point, the body starts falling freely due to gravity. The initial velocity of the body is the same as the velocity of the balloon when the body was released (1 m/s), but in the opposite direction (i.e., downwards). The acceleration acting on the body is the acceleration due to gravity, which is -g = -10 m/s^2 (negative since it acts downward).
Now, we can use the equations of motion to find the time taken for the body to reach the ground:
1. Equation for the motion of the balloon:
Velocity of balloon (v_b) = 1 m/s
Time (t) = 4 seconds (since the body is released after 4 seconds)
2. Equation for the motion of the falling body:
Initial velocity of body (u_b') = -1 m/s (opposite direction of balloon's velocity)
Acceleration due to gravity (a) = -10 m/s^2
Distance covered by the body (s_b) = unknown
Time taken by the body to reach the ground (t_b) = unknown
Using the equation:
s_b = u_b' * t_b + (1/2) * a * t_b^2
Plugging in the values:
0 = -1 * t_b + (1/2) * (-10) * t_b^2
Simplifying the equation:
-t_b + (-5) * t_b^2 = 0
Now we can solve for t_b using this quadratic equation:
-5 * t_b^2 - t_b = 0
Factoring out t_b:
t_b * (-5 * t_b - 1) = 0
Setting each factor equal to zero:
t_b = 0 (this is not possible since the body has to fall for some time)
OR
-5 * t_b - 1 = 0
Solving for t_b:
-5 * t_b = 1
t_b = 1 / (-5)
t_b = -1/5 = -0.2 seconds
Since time cannot be negative, the value of t_b = -0.2 seconds is extraneous. Therefore, we can conclude that the time taken by the released body to reach the ground is 0 seconds.
This means that as soon as the body is released, it will instantly fall to the ground because it was already at a height of 0 meters when released.