5. A bomber is flying at a height of 9 km at 800 km/h. How far in front of the target should he
drop his bombs? show formulas*
800 km/h = 222.2 m/s
Bomb fall time = sqrt(2H/g) = 42.9 s
(neglecting air resistance)
Bomb forward motion during fall time =
42.9*222.2 = 9533 m = 9.53 km
That is the "lead distance"
Well, if I were a bomber, I wouldn't want to miss the target, so I'd drop the bombs right on top of it. But if you want to calculate the distance, we can use some helpful formulas.
We need to find the time it takes for the bombs to hit the ground. First, let's convert the bomber's speed from km/h to m/s, because we're gonna get technical like that. So, 800 km/h is approximately 222.22 m/s (rounded for comedic effect).
Now, we can use the formula: time = distance / speed. Since we want to find time, we can rearrange the formula to: distance = time * speed.
The time it takes for the bombs to hit the ground is the same time it takes for the bomber to fly 9 km (since he drops the bombs right when he's above the target). So, plugging in the values, we have:
distance = (9 km) / (222.22 m/s)
Let's convert the kilometers to meters because math loves consistency. 9 km is equivalent to 9000 meters. Now we can calculate:
distance = (9000 m) / (222.22 m/s)
Grab your calculators because it's time for some division! 9000 divided by 222.22 gives us approximately 40.506 seconds.
Therefore, the bomber should drop his bombs about 40.506 seconds in front of the target. But keep in mind, if you want precision, you might need to account for any wind or weather conditions up there. Good luck, Mr. Bomber!
To find the distance in front of the target where the bomber should drop its bombs, we need to calculate the time it takes for the bombs to reach the ground.
First, let's determine the time it takes for the bombs to fall from the height of 9 km (9000 meters). We can use the formula:
t = √(2h / g)
where:
t is the time in seconds,
h is the height in meters,
g is the acceleration due to gravity (approximately 9.8 m/s²).
Plugging in the values:
t = √(2 * 9000 m / 9.8 m/s²)
Next, we need to calculate how far the bomber travels during this time. We can use the formula:
distance = speed × time
where:
distance is the distance the bomber travels (the distance in front of the target they should drop the bombs),
speed is the speed of the bomber,
time is the time calculated from the previous step.
Plugging in the values:
distance = 800 km/h × (t/3600) hours
Note that we divide t by 3600 to convert seconds to hours, as the speed is given in kilometers per hour.
Now we can substitute the value of t from the first calculation into the distance formula to get the answer.