A missile is fired at an angle of 75 from the horizontal. At one point, its speed was 900 mph. Find its horizontal velocity in miles per minute. (Round to the nearest hundredth.)
More information is required. The speed varies during flight, so you'd need to know the time or altitude where the missile had the 900 mph speed.
If is is 900 mph at launch, that is 15 miles per minute, and the horizontal component is, and remains, 3.88 miles per minute
To find the horizontal velocity of the missile, we need to determine its horizontal component of velocity.
Given that the missile was fired at an angle of 75 degrees from the horizontal, we can use trigonometry to find the horizontal component of velocity.
The horizontal component of velocity can be determined using the formula:
v_x = v * cos(θ)
where
v_x is the horizontal component of velocity,
v is the initial velocity of the missile, and
θ is the angle at which the missile was fired.
Let's plug in the values:
v = 900 mph
θ = 75 degrees
v_x = 900 * cos(75)
To calculate this, we need to convert mph to miles per minute since the problem asks for the answer in miles per minute.
1 mph = 1/60 miles per minute
Substituting this conversion, we have:
v_x = (900 * (1/60)) * cos(75)
Now we can calculate the horizontal velocity.
To find the horizontal velocity of the missile in miles per minute, we can use trigonometry.
The horizontal velocity of an object in projectile motion remains constant throughout its motion. It does not depend on the angle of projection or the initial speed. Therefore, we can simply calculate the horizontal component of velocity.
Given that the speed of the missile is 900 mph, we need to find its horizontal velocity.
The horizontal and vertical velocities of an object can be calculated using the equations:
- Horizontal Velocity (Vx) = Velocity (V) * cos(angle)
- Vertical Velocity (Vy) = Velocity (V) * sin(angle)
Using the given values:
V = 900 mph
angle = 75 degrees
First, we need to convert the angle from degrees to radians, as trigonometric functions in math libraries typically use radians as input.
To convert degrees to radians, we use the formula:
radians = (degrees * π) / 180
Plugging in the values:
radians = (75 * π) / 180
Next, we can calculate the horizontal velocity using the formula:
Vx = V * cos(angle)
Plugging in the values:
Vx = 900 * cos(radians)
Once we have the horizontal velocity, we need to convert it from miles per hour to miles per minute because the question asks for the result in miles per minute.
To convert miles per hour to miles per minute, we divide by 60 (since there are 60 minutes in an hour).
Finally, round the answer to the nearest hundredth.
Now let's calculate it step by step.
Step 1: Convert the angle to radians
radians = (75 * π) / 180
radians ≈ 1.309 radians (rounded to three decimal places)
Step 2: Calculate the horizontal velocity
Vx = 900 * cos(1.309)
Vx ≈ 900 * 0.277
Vx ≈ 249.30 mph (rounded to two decimal places)
Step 3: Convert the horizontal velocity to miles per minute
Vx_mpm = 249.30 / 60
Vx_mpm ≈ 4.16 miles per minute (rounded to two decimal places)
Therefore, the horizontal velocity of the missile is approximately 4.16 miles per minute.