If a plane is 2.00km above ground, and is traveling at 250 m/s [east] when it drops a bomb, will the bomb blow up the target which is 5.05km [horizontal distance] from the place?
how long does it take to fall 2000m?
h=1/2 g t^2 solve for time t,in seconds.
How far horizontally does it travel?
distance=250m/s*time
To determine whether the bomb will blow up the target, we need to calculate the time it takes for the bomb to hit the ground and the horizontal distance it travels during that time.
First, let's determine the time it takes for the bomb to hit the ground. Since the plane is 2.00 km above the ground, the initial vertical velocity of the bomb is 0 m/s (assuming it is dropped without any initial upward or downward velocity). We can use the following kinematic equation to find the time (t) it takes for the bomb to fall:
h = (1/2) * g * t^2
Where:
h is the height (2.00 km = 2000 m)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time
Rearranging the equation, we get:
t = sqrt((2 * h) / g)
Plugging in the values:
t = sqrt((2 * 2000) / 9.8) = sqrt(4000 / 9.8) ≈ 20.2 seconds
Now, let's calculate the horizontal distance the bomb travels in that time. The horizontal velocity of the bomb is given as 250 m/s [east], and the time of flight is 20.2 seconds. We can use the formula:
distance = velocity * time
So, the horizontal distance covered by the bomb is:
distance = 250 m/s * 20.2 s = 5050 meters = 5.05 km
The horizontal distance matches the distance to the target, which means the bomb will blow up the target, given the assumptions and calculations made.