A missile is fired at an angle of 85 from the horizontal. At one point, its speed was 1,000 mph. Find its horizontal velocity in miles per minute
What is 1000*cos85
87.16
To find the horizontal velocity of the missile, we need to decompose the initial velocity into its horizontal and vertical components.
Given:
Initial angle of the missile with respect to the horizontal, θ = 85 degrees
Initial speed of the missile, v = 1,000 mph
To find the horizontal velocity component (Vx), we can use the equation:
Vx = v * cos(θ)
First, we need to convert the angle from degrees to radians:
θ_radians = θ * π / 180
Now, we can substitute the values into the equation and calculate the horizontal velocity:
Vx = 1000 * cos(85 * π / 180)
To convert the velocity from mph to miles per minute, we need to divide by 60 since there are 60 minutes in an hour.
Vx_miles_per_minute = Vx / 60
Let's calculate the value of Vx_miles_per_minute.
To find the horizontal velocity of the missile, we need to calculate the horizontal component of its velocity.
The velocity of an object can be described using its horizontal component (Vx) and vertical component (Vy). In this case, we are interested in the horizontal component.
Given that the missile was fired at an angle of 85 degrees from the horizontal, we can use trigonometry to relate the velocity components.
The horizontal component of the velocity (Vx) can be calculated using the equation:
Vx = V * cos(θ),
where V is the magnitude of the velocity and θ is the angle with the horizontal.
In this case, the magnitude of the velocity is given as 1,000 mph, and the angle is 85 degrees.
First, we need to convert mph to m/s since the SI unit for velocity is meters per second.
1 mile = 1.60934 km (conversion factor)
1 km = 1000 meters (conversion factor)
1 hour = 3600 seconds (conversion factor)
So, 1 mph ≈ (1.60934 * 1000) / 3600 m/s.
Now we can calculate the horizontal velocity:
Vx = (1,000 mph) * cos(85 degrees).
To convert mph to m/s:
Vx = (1,000 * (1.60934 * 1000) / 3600) m/s ≈ 447.04 m/s.
Finally, since we want the horizontal velocity in miles per minute, we can convert m/s to mph:
1 mile ≈ 0.00062137119223733 miles (conversion factor)
1 minute ≈ 60 seconds (conversion factor)
So, the horizontal velocity is approximately:
Vx = 447.04 m/s * (0.00062137119223733 * 3600) / 60 mph ≈ 16.99 mph.
Therefore, the horizontal velocity of the missile is approximately 16.99 mph.