a missile is launched an angle of 26.5 with respect to the horizontal. if it travels in the straight line over the level Terran for 2 minute and its average speed is 6000 mile per hour. what is its altitude?
Assume:
1. no air resistance
2. initial speed (Vi) = "average speed" = 6000 mph
Change in vertical altitude after time t
=Vi*sin(θ)t - (1/2)gt²
Vi = initial velocity = 6000 mph = 8800 ft/s
t=time since launch = 120 s.
θ=launch angle above horizontal = 26.5°
g=acceleration due to gravity = 32.2 ft/s²
Work with feet and seconds.
To determine the missile's altitude, we need to use trigonometry. Here are the steps to find the altitude:
1. Convert the speed from miles per hour to miles per minute, since we know the time traveled in minutes. To do this, divide the average speed by 60 (since there are 60 minutes in an hour):
Speed (miles per minute) = 6000 miles/hour ÷ 60 minutes/hour = 100 miles/minute
2. Since we know the speed and time of travel, we can calculate the distance covered by multiplying the speed by time:
Distance = Speed × Time = 100 miles/minute × 2 minutes = 200 miles
3. Next, we can use trigonometry to find the altitude. The vertical distance (altitude) is represented by the opposite side of the angle of 26.5 degrees. The adjacent side represents the horizontal distance traveled.
4. We need to find the opposite side of the triangle. We can use the sine function to calculate this value:
Sin(26.5°) = Opposite / Hypotenuse
We know the hypotenuse is the distance covered (200 miles), so we can rearrange the equation to solve for the opposite side (altitude):
Opposite = Sin(26.5°) × Hypotenuse
Opposite = Sin(26.5°) × 200 miles
5. Finally, calculate the value of the opposite (altitude):
Altitude = Sin(26.5°) × 200 miles
Using a calculator, find Sin(26.5°) and multiply it by 200 miles to determine the missile's altitude.