A bomb dropped from a balloon reaches the ground in 30seconds.Determine the height of the balloon if it is ascending with a speed of 100cm^-1 when the bomb is dropped.
To determine the height of the balloon, we'll need to use the formula for the distance an object travels when accelerated.
The formula is given by:
S = ut + (1/2)at^2
Where:
S = distance
u = initial velocity
t = time
a = acceleration
In this case, the balloon is ascending at a speed of 100 cm/s, so the initial velocity (u) is +100 cm/s (upwards direction). The acceleration (a) is the acceleration due to gravity, which is usually -9.8 m/s^2 (downwards direction). However, we need to convert the units to match the units of time.
Given that the time (t) is 30 seconds, we can now substitute these values into the equation:
S = ut + (1/2)at^2
Notice that we need to convert the units to be consistent. We'll convert cm/s to m/s:
1 cm = 0.01 m
1 s = 1 s
So, u = 100 cm/s = 100 * 0.01 m/s = 1 m/s
a = -9.8 m/s^2 (since we are considering the direction as downwards)
Substituting these values in:
S = (1 m/s)(30 s) + (1/2)(-9.8 m/s^2)(30 s)^2
Simplifying further:
S = 30 m - (1/2)(9.8 m/s^2)(900 s^2)
S = 30 m - 4410 m
S = -4380 m
Since the balloon is ascending, the distance traveled is upwards, which corresponds to a negative value in this equation. Therefore, the height of the balloon is 4380 meters above the ground.
recall that the standard equation of motion means that you will solve for h in
h(t) = h + vt - 4.9 t^2 = 0
Just plug in your initial speed v and time = 30, then solve for h.