A missile is fired with a launch velocity of 15000 ft/s at a target 1200 miles away. How long after it is fired will the target be hit? Use g = 32 ft/s.s Express your answer in seconds
You have posted this same problem several times. What is the issue here? At this point, you are spamming the board. Either state what you can't understand from the previous answers, or go somewhere else, all I can see is you are wanting to graze for answers.
Maybe try changing the school subject, and stop spamming I can see at least five times that you posted this.
To determine how long it will take for the missile to hit the target, we can use the formula for motion in one dimension:
distance = initial velocity × time + (1/2) × acceleration × time^2.
In this case, the initial velocity is 15000 ft/s, the target distance is 1200 miles, and the acceleration due to gravity (g) is 32 ft/s^2.
First, let's convert the target distance from miles to feet:
1200 miles = 1200 miles × 5280 ft/mile = 6,336,000 ft.
Now, we can rearrange the formula to solve for time:
distance = initial velocity × time + (1/2) × acceleration × time^2.
Rearranging the terms:
(1/2) × acceleration × time^2 + initial velocity × time - distance = 0.
Using the quadratic formula:
time = (-initial velocity ± sqrt(initial velocity^2 - 4 × (1/2) × acceleration × -distance)) / (2 × (1/2) × acceleration).
Simplifying the formula:
time = (-initial velocity ± sqrt(initial velocity^2 + 2 × acceleration × distance)) / acceleration.
Substituting the values:
time = (-15000 ± sqrt(15000^2 + 2 × 32 × 6,336,000)) / 32.
Calculating inside the square root:
time = (-15000 ± sqrt(225,000,000 + 406,272,000)) / 32.
time = (-15000 ± sqrt(631,272,000)) / 32.
time = (-15000 ± 25,131.59) / 32.
Solving for both options:
time1 = (-15000 + 25,131.59) / 32.
time2 = (-15000 - 25,131.59) / 32.
Calculating:
time1 = 580.11 s.
time2 = -1102.87 s.
Since time cannot be negative in this context, we can discard the negative value.
Therefore, the missile will hit the target approximately 580.11 seconds after it is fired.